AGH USTFaculty of Applied Mathematics
.01

PERSONAL DETAILS

I am Full Professor of Mathematics at Faculty of Applied Mathematics of AGH University of Science and Technology. From September 2020 till June 2022 I was Dean of the Faculty.

I am a member of the Committee of Mathematics of the Polish Academy of Sciences (term 2016-2019) and member of its Presidium from 2019.

I was member of the senate of AGH University, terms 2012-2016 and 2016-2020.

I am member of Scientific Council (terms 2015-2018 and 2019-2022) of Juliusz P. Schauder Center for Nonlinear Studies.

In years 2013-2015 I was the Chairman of Young Scientists Council, a subsidiary body of the Minister of Science and Higher Education.

I am currently engaged in multiple projects in the field of Mathematics and Applied Mathematics, with main focus on Qualitative Theory of Dynamical Systems.

ORCID: 0000-0002-0261-7229
ResearcherID: A-2099-2009
Scopus: 14040447800
MR Author ID: 765606
Researchgate profile
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## RESEARCH

My research concentrates on the following topics:

Topological theory of discrete dynamical systems, low dimensional dynamical systems, chaos and entropy, symbolic dynamics (shift spaces), surface dynamics, ergodic theory, continuum theory.

My closest research team at AGH consists of PhD students and postdoctoral researchers funded from external projects. I also closely collaborate with several other mathematicians from AGH who are interested in broadly understood field of dynamical systems. Beyond this, I collaborate with colleagues from other departments, sharing my mathematical experience in various interdisciplinary teams.

During years I developed a large network of collaborators all over the world, from many different countries on all continents. This statement is confirmed by extensive list of collaborators of my papers. I am very happy that I was given a chance to collaborate with so many excellent mathematicians.

RESEARCH PROJECTS

Project studies structural properties of dynamical systems, that is structures obtained as long-term results of iterations of continuous functions. Our main analysis is focused on commonly accepted measures of complexity of structure of orbits (e.g. so-called entropy) and mathematical tools helping to decide if an object (e.g. visualized on computer screen) has complicated or simple structure (these tools are provided by branch of mathematics called topology). First, we will develop techniques allowing us to construct complicated objects with particualr properties. Very important tool in this matter will be (some versions) of shadowing property. Very roughly speaking, shadowing property ensures that results we draw on computer screen reflect real behaviour in the system under investigation. Project aims to provide very deep insight into mathematical aspects of dynamical complexity. To reach this aim, we will employ many different advanced mathematical techniques, that originated from topology and ergodic theory, using recent mathematical advances and open problems as starting point of our study.

Grant from National Science Center (NCN), project no. 2019/35/B/ST1/02239

### Limit sets of discrete dynamical systems

#### LISEDIDYS

The proposed project aims to deepen our knowledge on limit sets which will provide a better understanding of the long term behavior of a discrete dynamical system. We will investigate the topological size and structure of basins of limit sets and study the properties of statistical limit sets and limit sets of backward trajectories. We will search for a criterion allowing to decide whether a given closed invariant set is a limit set of some backward trajectory. The focus will be on the low- dimensional dynamical systems such as interval maps, maps acting on the circle, graphs, dendrites, Cantor space. We will use methods and techniques from topological dynamics and ergodic theory, including combinatorial and symbolic dynamics, shadowing, specification property, invariant measures and generic points.

Grant in H2020 within call MGA MSCA-IF to host Jana Hantáková at AGH
Project no. 883748
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## RESEARCH TEAM

My closest research team, performing research under my guidance as a grant PI/supervisor is listed below. It is placed within a larger Dynamical Systems group at AGH, so my local group of collaborators is much larger. In practice, huge part of our research is done in collaboration with many mathematicians from various research groups at many universities all over the world.

Silvère Gangloff
Postdoctoral Researcher
Jernej Činč
Visiting Professor
Łukasz Czech
PhD student
Łukasz Cholewa
PhD student
Domagoj Jelić
PhD student
Jakub Tomaszewski
PhD student

FORMER PHD STUDENTS

During my career I collaborated with many young, promising mathematicians. The ones listed below make me especially proud, as my children in science (see Math Genealogy Project).

Magdalena Foryś-Krawiec
PhD 2016
Paweł Potorski
PhD 2019
Tomasz Drwięga
PhD 2019

FORMER POSTDOCS

Jana Hantáková
Marie-Curie Fellow
.04

## PUBLICATIONS

133

### All publications

PUBLICATIONS LIST
2022

### On recurrence and entropy in hyperspace of continua in dimension one

Unpublished manuscript

Preprint Domagoj Jelić and Piotr Oprocha

### On recurrence and entropy in hyperspace of continua in dimension one

Domagoj Jelić and Piotr Oprocha
Preprint
We show that if G is a topological graph, and f is contin-
uous map, then the induced map f acting on the hyperspace C(G) of
all connected subsets of G by natural formula f (C) = f (C) carries the
same entropy as f . This is well known that it does not hold on the larger
hyperspace of all compact subsets. Also negative examples were given
for the hyperspace C(X) on some continua X, including dendrites.
Our work extends previous positive results obtained first for much
simpler case of compact interval by completely different tools.
2022

### Are generic dynamical properties stable under composition with rotations?

#### Arxiv

Unpublished manuscript

Preprint J. Bobok, J. Činč, P. Oprocha, S. Troubetzkoy

### Are generic dynamical properties stable under composition with rotations?

J. Bobok, J. Činč, P. Oprocha, S. Troubetzkoy
Preprint
In this paper we provide a detailed topological and measure-theoretic study of Lebesgue measure-preserving circle maps that are rotated with inner and outer rotations which are independent of each other. In particular, we analyze the stability of the locally eventually onto and measure-theoretic mixing properties.
2022

### Parametrized family of pseudo-arc attractors: physical measures and prime end rotations

#### PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY

125(2) (2022), 318-357.

Journal Paper Jernej Činč, Piotr Oprocha

### Parametrized family of pseudo-arc attractors: physical measures and prime end rotations

Jernej Činč, Piotr Oprocha
Journal Paper
The main goal of this paper is to study topological and measure-theoretic properties of an intriguing family of strange planar attractors. Building towards these results, we first show that any generic Lebesgue measure preserving map f generates the pseudo-arc as inverse limit with f as a single bonding map. These maps can be realized as attractors of disc homeomorphisms in such a way that the attractors vary continuously (in Hausdorff distance on the disc) with the change of bonding map as a parameter. Furthermore, for generic Lebesgue measure preserving maps f the background Oxtoby-Ulam measures induced by Lebesgue measure for f on the interval are physical on the disc and in addition there is a dense set of maps f defining a unique physical measure. Moreover, the family of physical measures on the attractors varies continuously in the weak* topology; i.e. the parametrized family is statistically stable. We also find an arc in the generic Lebesgue measure preserving set of maps and construct a family of disk homeomorphisms parametrized by this arc which induces a continuously varying family of pseudo-arc attractors with prime ends rotation numbers varying continuously in [0,1/2]. It follows that there are infinitely many dynamically non-equivalent embeddings of the pseudo-arc in this family of attractors
2021

### Beyond 0 and ∞: A solution to the Barge Entropy Conjecture

#### Arxiv

Unpublished manuscript

Preprint J. Boroński, J. Činč, P. Oprocha

### Beyond 0 and ∞: A solution to the Barge Entropy Conjecture

J. Boroński, J. Činč, P. Oprocha
Preprint
We prove the entropy conjecture of M. Barge from 1989: for every r ∈ [0, ∞] there exists a pseudo-arc homeomorphism h, whose topological entropy is r. Until now all pseudo-arc homeomorphisms with known entropy have had entropy 0 or ∞.
2022

### On automatic calibration of the SIRD epidemiological model for COVID-19 data in Poland

#### Arxiv

Unpublished manuscript

P. Błaszczyk, K. Klimczak, A. Mahdi, P. Oprocha, P. Potorski, P. Przybyłowicz, M. Sobieraj

### On automatic calibration of the SIRD epidemiological model for COVID-19 data in Poland

P. Błaszczyk, K. Klimczak, A. Mahdi, P. Oprocha, P. Potorski, P. Przybyłowicz, M. Sobieraj
2022

### On mathematical aspects of evolution of dislocation density in metallic materials

#### IEEE Access

10 (2022), 86793 - 86812.

Journal Paper N. Czyżewska, J. Kusiak, P. Morkisz, P. Oprocha, M. Pietrzyk, P. Przybyłowicz, Ł. Rauch, D. Szeliga

### On mathematical aspects of evolution of dislocation density in metallic materials

N. Czyżewska, J. Kusiak, P. Morkisz, P. Oprocha, M. Pietrzyk, P. Przybyłowicz, Ł. Rauch, D. Szeliga
Journal Paper
This paper deals with the solution of delay differential equations describing evolution of dislocation density in metallic materials. Hardening, restoration, and recrystallization characterizing the evolution of dislocation populations provide the essential equation of the model. The last term trans- forms ordinary differential equation (ODE) into delay differential equation (DDE) with strong (in general, Hölder) nonlinearity. We prove upper error bounds for the explicit Euler method, under the assumption that the right- hand side function is Hölder continuous and monotone which allows us to com- pare accuracy of other numerical methods in our model (e.g. Runge-Kutta), in particular when explicit formulas for solutions are not known. Finally, we test the above results in simulations of real industrial process.
2022

### Periodic points and shadowing property for generic Lebesgue measure preserving interval maps

#### Nonlinearity

35(5) (2022), article id: 2534

Journal Paper Jozef Bobok, Jernej Činč, Piotr Oprocha, Serge Troubetzkoy

### Periodic points and shadowing property for generic Lebesgue measure preserving interval maps

Jozef Bobok, Jernej Činč, Piotr Oprocha, Serge Troubetzkoy
Journal Paper
We show that for the generic continuous maps of the interval and circle which preserve the Lebesgue measure it holds for each k 1 that the set of periodic points of period k is a Cantor set of Hausdorff dimension zero and of upper box dimension one. Furthermore, building on this result, we show that there is a dense collection of transitive Lebesgue measure preserving interval map whose periodic points have full Lebesgue measure and whose periodic points of period k have positive measure for each k 1. Finally, we show that the generic continuous maps of the interval which preserve the Lebesgue measure satisfy the shadowing and periodic shadowing property.
2022

### Stochastic model describing evolution of microstructural parameters during hot rolling of steel plates and strips

#### ARCHIVES OF CIVIL AND MECHANICAL ENGINEERING

22(3) (2022), Article id: 139.

Journal Paper D. Szeliga, N. Czyzewska, K. Klimczak, J. Kusiak, R. Kuziak, P. Morkisz, P. Oprocha, M. Pietrzyk, L Poloczek, P. Przybylowicz

### Stochastic model describing evolution of microstructural parameters during hot rolling of steel plates and strips

D. Szeliga, N. Czyzewska, K. Klimczak, J. Kusiak, R. Kuziak, P. Morkisz, P. Oprocha, M. Pietrzyk, L Poloczek, P. Przybylowicz
Journal Paper
Enhancing strength-ductility synergy of materials has been for decades an objective of research on structural metallic materials. It has been shown by many researchers that significant improvement of this synergy can be obtained by tailoring heterogeneous multiphase microstructures. Since large gradients of properties in these microstructures cause a decrease of the local fracture resistance, the objective of research is to obtain smoother gradients of properties by control of the manufacturing process. Advanced material models are needed to design such microstructures with smooth gradients. These models should supply information about distributions of various microstructural features, instead of their average values. Models based on stochastic internal variables meet this requirement. Our objective was to account for the random character of the recrystallization and to transfer this randomness into equations describing the evolution of dislocations and grain size during hot deformation and during interpass times. The idea of this stochastic model is described in the paper. Experiments composed of uniaxial compression tests were performed to supply data for the identification and verification of the model in the hot deformation and static recrystallization parts. Histograms of the grain size were measured after hot deformation and at different times after the end of deformation. Identification and validation of the model were performed. The validated model, which predicts evolution of heterogeneous multiphase microstructure, is the main output of our work. The model was implemented in the finite element program for hot rolling of plates and sheets and simulations of these processes were performed. The model’s capability to compare and evaluate various rolling strategies are demonstrated in the paper.
2022

### Formulation, identification and validation of a stochastic internal variables model describing the evolution of metallic materials microstructure during hot forming

#### INTERNATIONAL JOURNAL OF MATERIAL FORMING

15(4) (2022), Article id: 53.

Journal Paper D. Szeliga, N. Czyzewska, K. Klimczak, J. Kusiak, R. Kuziak, P. Morkisz, P. Oprocha, V. Pidvysots'kyy, M. Pietrzyk, P. Przybylowicz.

### Formulation, identification and validation of a stochastic internal variables model describing the evolution of metallic materials microstructure during hot forming

D. Szeliga, N. Czyzewska, K. Klimczak, J. Kusiak, R. Kuziak, P. Morkisz, P. Oprocha, V. Pidvysots'kyy, M. Pietrzyk, P. Przybylowicz.
Journal Paper
Construction metallic materials combine strength with formability. These features are obtained for heterogeneous microstructures with hard constituents dispersed in a soft matrix. On the other hand, sharp gradients of properties between phases cause a local fracture. Advanced models are needed to design microstructures with smoother gradients of their features. Models based on stochastic internal variables meet this requirement. Our objective was to account for the random character of the recrystallization and to transfer this randomness to equations describing the evolution of dislocations and grain size. The idea of the internal variable model with dislocation density and grain size being stochastic variables is described in the paper. Experiments composed of uniaxial compression tests were performed to supply data for the identification and verification of the model. The loads as a function of time during compression and histograms of the grain size after deformation were measured in each test. Identification and validation of the model were performed. Finally, the developed model was applied to simulate selected industrial hot forming processes.
2021

### New exotic minimal sets from pseudo-suspensions of Cantor systems

#### Journal of Dynamics and Differential Equations

Published online

Journal PaperPreprint J. Boroński, A. Clark, P. Oprocha

### New exotic minimal sets from pseudo-suspensions of Cantor systems

J. Boroński, A. Clark, P. Oprocha
Journal PaperPreprint
We develop a technique, pseudo-suspension, that applies to invariant sets of homeomorphisms of a class of annulus homeomorphisms we describe, Handel-Anosov-Katok (HAK) homeomorphisms, that generalize the homeomorphism first described by Handel. Given a HAK homeomorphism and a homeomorphism of the Cantor set, the pseudo-suspension yields a homeomorphism of a new space that admits a homeomorphism that combines features of both of the original homeomorphisms. This allows us to answer a well known open question by providing examples of hereditarily indecomposable continua that admit homeomorphisms of intermediate complexity. Additionally, we show that such examples occur as minimal sets of volume preserving smooth diffeomorphisms of 4-dimensional manifolds. We also use our techniques to exhibit the first examples of minimal, uniformly rigid and weakly mixing homeomorphisms in dimension 1, and these can also be realized as invariant sets of smooth diffeomorphisms of a 4-manifold. Until now the only known examples of spaces that admit minimal, uniformly rigid and weakly mixing homeomorphisms were modifications of those given by Glasner and Maon in dimension at least 2.
2021

### Renormalization in Lorenz maps – completely invariant sets and periodic orbits

#### Arxiv

Unpublished manuscript

Preprint Ł. Cholewa, P. Oprocha

### Renormalization in Lorenz maps – completely invariant sets and periodic orbits

Ł. Cholewa, P. Oprocha
Preprint
The paper deals with dynamics of expanding Lorenz maps, which appear in a natural way as Poincar\`e maps in geometric models of well-known Lorenz attractor. We study connections between periodic points, completely invariant sets and renormalizations. We show that in general, renormalization cannot be fully characterized by a completely invariant set, however there are various situations when such characterization is possible. This way we provide a better insight into the structure of renormalizations in Lorenz maps, correcting some gaps existing in the literature and completing to some extent the description of possible dynamics in this important field of study.
2022

### Multiorders in amenable group actions

#### Groups, Geometry, and Dynamics

Accepted for publication

Journal PaperPreprint Tomasz Downarowicz, Piotr Oprocha, Mateusz Więcek, Guohua Zhang

### Multiorders in amenable group actions

Tomasz Downarowicz, Piotr Oprocha, Mateusz Więcek, Guohua Zhang
Journal PaperPreprint
The paper offers a thorough study of multiorders and their applications to measure-preserving actions of countable amenable groups. By a multiorder on a countable group we mean any probability measure ν on the collection O of linear orders of type Z on G, invariant under the natural action of G on such orders. Every free measure-preserving G-action (X,μ,G) has a multiorder (O,ν,G) as a factor and has the same orbits as the Z-action (X,μ,S), where S is the successor map determined by the multiorder factor. The sub-sigma-algebra ΣO associated with the multiorder factor is invariant under S, which makes the corresponding Z-action (O,ν,S) a factor of (X,μ,S). We prove that the entropy of any G-process generated by a finite partition of X, conditional with respect to ΣO, is preserved by the orbit equivalence with (X,μ,S). Furthermore, this entropy can be computed in terms of the so-called random past, by a formula analogous to the one known for Z-actions. This fact is applied to prove a variant of a result by Rudolph and Weiss. The original theorem states that orbit equivalence between free actions of countable amenable groups preserves conditional entropy with respect to a sub-sigma-algebra Σ, as soon as the “orbit change” is Σ-measurable. In our variant, we replace the measurability assumption by a simpler one: Σ should be invariant under both actions and the actions on the resulting factor should be free. In conclusion we prove that the Pinsker sigma-algebra of any G-process can be identified (with probability 1) using the following algorithm: (1) fix an arbitrary multiorder on G, (2) select any order from the support of that multiorder, (3) in the process, find the “remote past” along the selected order
2022

### Quasi-graphs, zero entropy and measures with discrete spectrum

#### Nonlinearity

35(3) (2022), article id: 1360.

Journal Paper J. Li, P. Oprocha, G. Zhang

### Quasi-graphs, zero entropy and measures with discrete spectrum

J. Li, P. Oprocha, G. Zhang
Journal Paper
In this paper, we study dynamics of maps on quasi-graphs characterizing their invariant measures. In particular, we prove that every invariant measure of quasi-graph map with zero topological entropy has discrete spectrum. Additionally, we obtain an analog of Llibre-Misiurewicz’s result relating positive topological entropy with existence of topological horseshoes. We also study dynamics on dendrites and show that if a continuous map on a dendrite, whose set of all endpoints is closed and has only finitely many accumulation points, has zero topological entropy, then every invariant measure supported on an orbit closure has discrete spectrum.
2022

### On the structure of alpha-limit sets of backward trajectories for graph maps

#### Discrete and Continuous Dynamical Systems

42(3) (2022), 1435-1463.

Journal Paper M. Foryś-Krawiec, J. Hantáková, P. Oprocha

### On the structure of alpha-limit sets of backward trajectories for graph maps

M. Foryś-Krawiec, J. Hantáková, P. Oprocha
Journal Paper
In the paper we study what sets can be obtained as α-limit sets of backward trajectories in graph maps. We show that in the case of mixing maps, all those α-limit sets are ω-limit sets and for all but finitely many points x, we can obtain every ω-limits set as the α-limit set of a backward trajectory starting in x. For zero entropy maps, every α-limit set of a backward trajectory is a minimal set. In the case of maps with positive entropy, we obtain a partial characterization which is very close to complete picture of the possible situations.
2021

### Graph maps with zero topological entropy and sequence entropy pairs

#### Proceedings of the American Mathematical Society

149(11) (2021), 4757–4770

Journal Paper J. Li, X. Liang, P. Oprocha

### Graph maps with zero topological entropy and sequence entropy pairs

J. Li, X. Liang, P. Oprocha
Journal Paper
We show that graph map with zero topological entropy is Li-Yorke chaotic if and only if it has an NS-pair (a pair of non-separable points containing in a same solenoidal ω-limit set), and a non-diagonal pair is an NS-pair if and only if it is an IN-pair if and only if it is an IT-pair. This completes characterization of zero topological sequence entropy for graph maps.
2021

### On alpha-limit sets in Lorenz maps

#### Entropy

23(9) (2021), article id: 1153

Journal Paper Łukasz Cholewa, Piotr Oprocha

### On alpha-limit sets in Lorenz maps

Łukasz Cholewa, Piotr Oprocha
Journal Paper
The aim of this paper is to show that alpha-limit sets in Lorenz maps do not have to be completely invariant. This highlights unexpected dynamical behavior in these maps, showing gaps existing in the literature. Similar result is obtained for unimodal maps on [0,1]. On the basis of provided examples, we also present how closely performed study on the structure of alpha-limit sets is connected with calculation of the topological entropy.
2021

### Sensitivity analysis, identification and validation of the dislocation density-based model for metallic materials

#### Metallurgical Research & Technology

118 (2021). article id: 317.

Journal Paper D. Szeliga, N. Czyżewska, K. Klimczak, J. Kusiak, P. Morkisz, P. Oprocha, M. Pietrzyk, P. Przybyłowicz

### Sensitivity analysis, identification and validation of the dislocation density-based model for metallic materials

D. Szeliga, N. Czyżewska, K. Klimczak, J. Kusiak, P. Morkisz, P. Oprocha, M. Pietrzyk, P. Przybyłowicz
Journal Paper
Microstructure evolution model based on the differential equation describing evolution of dislocations was proposed. Sensitivity analysis was performed and parameters with the strongest influence on the output of the model were revealed. Identification of the model coefficients was performed for various metallic materials using inverse analysis for experimental data. The model was implemented in the finite element code and simulations of various hot forming processes were performed.
2021

### A Cantor dynamical system is slow if and only if all its finite orbits are attracting

#### Discrete and Continuous Dynamical Systems

42(6) (2022), 3039-3064.

Journal Paper S. Gangloff, P. Oprocha

### A Cantor dynamical system is slow if and only if all its finite orbits are attracting

S. Gangloff, P. Oprocha
Journal Paper
In this paper we completely solve the problem when a Cantor dynamical system (X,f) can be embedded in R with vanishing derivative everywhere. For this purpose we construct a refining sequence of marked clopen partitions of X which is adapted to a dynamical system of this kind. It turn out that there is a huge class of such systems.
2021

### S-limit shadowing is generic for continuous Lebesgue measure preserving circle maps

#### Ergodic Theory and Dynamical Systems

Published on-line

Journal PaperPreprint Jozef Bobok, Jernej Činč, Piotr Oprocha, Serge Troubetzkoy

### S-limit shadowing is generic for continuous Lebesgue measure preserving circle maps

Jozef Bobok, Jernej Činč, Piotr Oprocha, Serge Troubetzkoy
Journal PaperPreprint
In this paper we show that generic continuous Lebesgue measure preserving circle maps have the s-limit shadowing property. In addition we obtain that s-limit shadowing is a generic property also for continuous circle maps. In particular, this implies that classical shadowing, periodic shadowing and limit shadowing are generic in these two settings as well.
2021

### Dendrites and measures with discrete spectrum

#### Ergodic Theory and Dynamical Systems

Published on-line

Journal PaperPreprint M. Foryś-Krawiec, J. Hantáková, J. Kupka, P. Oprocha, S. Roth

### Dendrites and measures with discrete spectrum

M. Foryś-Krawiec, J. Hantáková, J. Kupka, P. Oprocha, S. Roth
Journal PaperPreprint
We are interested in dendrites for which all invariant measures of zero-entropy mappings have discrete spectrum, and we prove that this holds when the closure of the endpoint set of the dendrite is countable. This solves an open question which was around for awhile, almost completing the characterization of dendrites with this property.
2021

### Inverse problem in stochastic approach to modelling of microstructural parameters in metallic materials during processing

#### Mathematical Problems in Engineering

Volume 2022, Article ID 9690742

Journal Paper K. Klimczak, P. Oprocha, J. Kusiak, D. Szeliga, P. Morkisz, P. Przybyłowicz, N. Czyżewska, M. Pietrzyk

### Inverse problem in stochastic approach to modelling of microstructural parameters in metallic materials during processing

K. Klimczak, P. Oprocha, J. Kusiak, D. Szeliga, P. Morkisz, P. Przybyłowicz, N. Czyżewska, M. Pietrzyk
Journal Paper
2021

### Minimal non-invertible maps on the pseudo-circle

#### Journal of Dynamics and Differential Equations

33 (2021), 1897–1916.

Journal Paper J. Boroński, J. Kennedy, X. Liu, P. Oprocha

### Minimal non-invertible maps on the pseudo-circle

J. Boroński, J. Kennedy, X. Liu, P. Oprocha
Journal Paper
In this article we show that R.H. Bing’s pseudo-circle admits a minimal non-invertible map. This resolves a conjecture raised by Bruin, Kolyada and Snoha in the negative. The main tool is a variant of the Denjoy–Rees technique, further developed by Béguin–Crovisier–Le Roux, combined with detailed study of the structure of the pseudo-circle. This is the first example of a planar 1-dimensional space that admits both minimal homeomorphisms and minimal noninvertible maps.
2021

### On entropy of Φ-irregular and Φ-level sets in maps with the shadowing property

#### Discrete and Continuous Dynamical Systems - A

41(3) (2021), 1271-1296.

Journal Paper M. Foryś-Krawiec, J. Kupka, P. Oprocha, X. Tian

### On entropy of Φ-irregular and Φ-level sets in maps with the shadowing property

M. Foryś-Krawiec, J. Kupka, P. Oprocha, X. Tian
Journal Paper
We study the properties of Φ-irregular sets (sets of points for which the Birkhoff average diverges) in dynamical systems with the shadowing property. We estimate the topological entropy of Φ-irregular set in terms of entropy on chain recurrent classes and prove that Φ-irregular sets of full entropy are typical. We also consider Φ-level sets (sets of points whose Birkhoff average is in a specified interval), relating entropy they carry with the entropy of some ergodic measures. Finally, we study the problem of large deviations considering the level sets with respect to reference measures.
2020

### Shadowing is generic on various one-dimensional continua with a special geometric structure

#### Journal of Geometric Analysis

30 (2020), 1836–1864.

Journal Paper P. Kościelniak, M. Mazur, P. Oprocha, Ł. Kubica

### Shadowing is generic on various one-dimensional continua with a special geometric structure

P. Kościelniak, M. Mazur, P. Oprocha, Ł. Kubica
Journal Paper
In the paper we use a special geometric structure of selected one-dimensional continua to prove that some stronger versions of the shadowing property are generic (or at least dense) for continuous maps acting on these spaces. Specifically, we prove that (i) the periodic 𝒯𝑆-bi-shadowing property, where 𝒯𝑆 means some class of continuous methods, is generic as well as the s-limit shadowing property is dense in the space of all continuous maps (and all continuous surjective maps) of any topological graph; (ii) the 𝒯𝑆-bi-shadowing property is generic as well as the s-limit shadowing property is dense in the space of all continuous maps of any dendrite; (iii) the 𝒯𝑆-bi-shadowing property is generic in the space of all continuous maps of chainable continuum that can by approximated by arcs from the inside. The results of the paper extend ones obtained over the last few decades by various authors (see, e.g., Kościelniak in J Math Anal Appl 310:188–196, 2005; Kościelniak and Mazur in J Differ Equ Appl 16:667–674, 2010; Kościelniak et al. in Discret Contin Dyn Syst 34:3591–3609, 2014; Mazur and Oprocha in J Math Anal Appl 408:465–475, 2013; Mizera in Generic Properties of One-Dimensional Dynamical Systems, Ergodic Theory and Related Topics, III, Springer, Berlin, 1992; Odani in Proc Am Math Soc 110:281–284, 1990; Pilyugin and Plamenevskaya in Topol Appl 97:253–266, 1999; and Yano in J Fac Sci Univ Tokyo Sect IA Math 34:51–55, 1987) for both homeomorphisms and continuous maps of compact manifolds, including (in particular) an interval and a circle, which are the simplest examples of one-dimensional continua. Moreover, from a technical point of view our considerations are a continuation of those carried out in the earlier work by Mazur and Oprocha in J. Math. Anal. Appl. 408:465–475, 2013.
2020

### Multi-sensitivity, multi-transitivity and Δ-transitivity

#### Contemporary Mathematics

In: Dynamics: Topology and Numbers
Contemporary Mathematics vol. 744
2020, pp. 231-244.

Book Chapter T. Yu, P. Oprocha, G. Zhang

### Multi-sensitivity, multi-transitivity and Δ-transitivity

T. Yu, P. Oprocha, G. Zhang
Book Chapter
In thispaper firstly we construct for each m∈N\{1} a weakly mixing system which is (1,…,m-1)-sensitive but not (1,…,m−1,m)-sensitive, and a minimal system which is (1,2)-sensitive but not (1,2,3)-sensitive. It is known that ∆-(1, 2) transitivity implies weak mixing. We will show that, though (a, b)-transitivity implies total transitivity for all a,b∈N, for a general vector a∈Nr, r ∈ N, ∆-a transitivity implies weak mixing if and only if the vector a satisfies certain conditions. Furthermore, we prove that this difference will disappear for measurable systems, that is, for measure-theoretical setting multi-ergodicity is equivalent to weak mixing.
2019

### All minimal Cantor systems are slow

#### Bulletin of the London Mathematical Society

51(6) (2019), 937-1128.

Journal Paper J. Boroński, J. Kupka, P. Oprocha

### All minimal Cantor systems are slow

J. Boroński, J. Kupka, P. Oprocha
Journal Paper
We show that every (invertible or noninvertible) minimal Cantor system embeds in with vanishing derivative everywhere. We also study relations between local shrinking and periodic points.
2019

### Mixing properties in expanding Lorenz maps

343 (2019), 712-755.

Journal PaperRepresentative publications P. Oprocha, P. Potorski, P. Raith

### Mixing properties in expanding Lorenz maps

P. Oprocha, P. Potorski, P. Raith
Journal PaperRepresentative publications
Let $T:[0,1]\to [0,1]$ be an expanding Lorenz map, this means $T x=f(x) \mod 1$ where $f: [0,1]\to [0,2]$ is a strictly increasing map satisfying $\inf f’>1$. Then $T$ has two pieces of monotonicity. In this paper, sufficient conditions when $\T$ is topologically mixing are provided. For the special case $f(x)=\beta x +\alpha$ with $\beta\geq \sqrt[3]{2}$ a full characterization of parameters $(\beta,\alpha)$ leading to mixing is given. Furthermore relations between renormalizability and $T$ being locally eventually onto are considered, and some gaps in classical results on the dynamics of Lorenz maps are corrected.
2019

### Mixing properties in coded systems

#### Springer Proceedings in Mathematics & Statistics

In: New Trends in One-Dimensional Dynamics
Springer Proceedings in Mathematics & Statistics vol 285.
2019, pp. 183-200

Conference proceedings J. Epperlein, D. Kwietniak, P. Oprocha

### Mixing properties in coded systems

J. Epperlein, D. Kwietniak, P. Oprocha
Conference proceedings
We show that topological mixing, weak mixing, the strong property P, and total transitivity are equivalent for coded systems (shift spaces presented by labeling the edges of a countable irreducible graphs by symbols from a finite alphabet). We provide an example of a topologically mixing coded system which cannot be approximated by any increasing sequence of topologically mixing shifts of finite type, has only periodic points of even period and each set of its generators consists of blocks of even length. We prove that such an example cannot be a synchronized system.
2019

### On the dynamics of generic maps on the Cantor set

#### Topology and its Applications

263 (2019), 330-342.

Journal Paper J. Kupka, P. Oprocha

### On the dynamics of generic maps on the Cantor set

J. Kupka, P. Oprocha
Journal Paper
Recently Bernardes and Darji provided a very nice characterization of a residual set of maps of Cantor set in terms of covers of special type. Using their characterization, we provide a more direct description of this class. This way we are able to provide a further characterization of dynamical properties (e.g. shadowing properties, nullness) of maps in the class and further study of what features (e.g. prescribed minimal sets or the values of topological entropy) we can get by small perturbations of a given homeomorphism.
2019

### ω-chaos without infinite LY-scrambled set on Gehman dendrite

#### International Journal of Bifurcation and Chaos

29(5) (2019), Article id: 05,195007.

Journal Paper T. Drwięga, P. Oprocha

### ω-chaos without infinite LY-scrambled set on Gehman dendrite

T. Drwięga, P. Oprocha
Journal Paper
We answer the last question left open in [Kočan, 2012] which asks whether there is a relation between an infinite LY-scrambled set and 𝜔-chaos for dendrite maps. We construct a continuous self-map of a dendrite without any infinite LY-scrambled set but containing an uncountable 𝜔-scrambled set.
2019

### Multi-criteria optimization strategies for tree-structured production chains

#### nternational Journal of Material Forming

12 (2019), 185-196.

Journal Paper P. Jarosz, J. Kusiak, S. Małecki, P. Morkisz, P. Oprocha, W. Piertucha and Ł. Sztangret

### Multi-criteria optimization strategies for tree-structured production chains

P. Jarosz, J. Kusiak, S. Małecki, P. Morkisz, P. Oprocha, W. Piertucha and Ł. Sztangret
Journal Paper
The aim of this paper is presentation of some optimization strategies applicable in the optimization of multi-stage and multi-thread chain structures (linear and tree-structured acyclic graphs) with multiple intermediate goal functions. The inspirations for this type of analysis are production chains often seen in industrial plants. Production in these plants consists of sequences of multiple units connected linearly or in tree-structured graphs in which, at various production stages, intermediate quality criteria, related to the semi-products, may have to be considered. Optimization strategies as well as the results of their application for different hypothetical problems and the real metallurgical problem of lead production are presented.
2019

#### Fundamenta Mathematicae

244 (2019), 287-312.

Journal Paper C. Good, P. Oprocha, M. Puljiz

C. Good, P. Oprocha, M. Puljiz
Journal Paper
We study three notions of shadowing: classical shadowing, limit (or asymptotic) shadowing, and s-limit shadowing. We show that classical and s-limit shadowing coincide for tent maps and, more generally, for piecewise linear interval maps with constant slopes, and are further equivalent to the linking property introduced by Chen in 1991. We also construct a system which exhibits shadowing but not limit shadowing, and we study how shadowing properties transfer to maximal transitive subsystems and inverse limits (sometimes called natural extensions). Where practicable, we show that our results are best possible by means of examples.
2019

### Double minimality, entropy and disjointness with all minimal systems

#### Discrete and Continuous Dynamical Systems - A

39 (2019), 263-275.

Journal Paper P. Oprocha

### Double minimality, entropy and disjointness with all minimal systems

P. Oprocha
Journal Paper
In this paper we propose a new sufficient condition for disjointness with all minimal systems. Using proposed approach we construct a transitive dynamical system (X,T) disjoint with every minimal system and such that the set of transfer times N(x,U) is not an IP-set for some nonempty open set UX and every xX. This example shows that the new condition sharpens sufficient conditions for disjointness below previous bounds. In particular our approach does not rely on distality of points or sets.
2019

### Mixing completely scrambled system exists

#### Ergodic Theory and Dynamical Systems

39(1) (2019), 62-73.

Journal PaperRepresentative publications J. Boroński, J. Kupka, P. Oprocha

### Mixing completely scrambled system exists

J. Boroński, J. Kupka, P. Oprocha
Journal PaperRepresentative publications
We prove that there exists a topologically mixing homeomorphism which is completely scrambled. We also prove that, for any integer n>0, there is a continuum of topological dimension n supporting a transitive completely scrambled homeomorphism and an n-dimensional compactum supporting a weakly mixing completely scrambled homeomorphism. This solves a 15-year-old open problem.
2019

### Prediction of Distribution of Microstructural Parameters in Metallic Materials Described by Differential Equations with Recrystallization Term

#### International Journal for Multiscale Computational Engineering

17 (2019), 361-371.

Journal Paper P. Morkisz, P. Oprocha, P. Przybyłowicz, N. Czyżewska, J. Kusiak, D. Szeliga, Ł. Rauch, M. Pietrzyk

### Prediction of Distribution of Microstructural Parameters in Metallic Materials Described by Differential Equations with Recrystallization Term

P. Morkisz, P. Oprocha, P. Przybyłowicz, N. Czyżewska, J. Kusiak, D. Szeliga, Ł. Rauch, M. Pietrzyk
Journal Paper
Continuous development of the transport industry is associated with the search for new construction materials that combine high strength with good plastic properties. Intensive research during the last few decades has shown that there is still a huge potential for improvement of properties of various metallic materials. New grades called advanced high strength steels (AHSS) with multiphase structures have been developed and widely used mainly in the automotive industry. These microstructures are characterized by large gradients of properties, which cause poor local formability. It is expected that materials with a more heterogeneous microstructure will have superior formability. More detailed models of the microstructure evolution are needed to answer this question. A hypothesis was made that application of the models based on internal variables allows for predictions of gradients of final product properties. The objectives of the present paper were two-fold. The first was to investigate the possibility of the analytical and numerical solutions of the evolution equation for the internal variable and evaluation of these solutions. We propose two numerical methods which give us an accurate approximation of the solution with relatively low computational cost at the same time. Implementation of the developed solutions in the finite element (FE) code and performing multiscale simulation of the evolution of internal variables during thermomechanical processing was the second objective of this paper. This solution supplied information about the distribution of the dislocation density in the volume of the material. Case studies for selected metal forming processes recapitulate the paper.
2018

### A compact minimal space Y such that its square YxY is not minimal

335 (2018), 261-275.

Journal PaperRepresentative publications J. Boroński, A. Clark, P. Oprocha

### A compact minimal space Y such that its square YxY is not minimal

J. Boroński, A. Clark, P. Oprocha
Journal PaperRepresentative publications
The following well known open problem is answered in the negative: Given two compact spaces X and Y that admit minimal homeomorphisms, must the Cartesian product admit a minimal homeomorphism as well? Moreover, it is shown that such spaces can be realized as minimal sets of torus homeomorphisms homotopic to the identity. A key element of our construction is an inverse limit approach inspired by combination of a technique of Aarts & Oversteegen and the construction of Slovak spaces by Downarowicz & Snoha & Tywoniuk. This approach allows us also to prove the following result. Let be a continuous, aperiodic minimal flow on the compact, finite-dimensional metric space M. Then there is a generic choice of parameters , such that the homeomorphism admits a noninvertible minimal map as an almost 1-1 extension
2018

### On the irregular points for systems with the shadowing property

#### Ergodic Theory and Dynamical Systems

38(6) (2018), 2108-2131.

Journal Paper Y. Dong, P. Oprocha, X. Tian

### On the irregular points for systems with the shadowing property

Y. Dong, P. Oprocha, X. Tian
Journal Paper
We prove that when f is a continuous self-map acting on a compact metric space (X, d) that satisfies the shadowing property, then the set of irregular points (i.e., points with divergent Birkhoff averages) has full entropy. Using this fact, we prove that, in the class of C-0-generic maps on manifolds, we can only observe (in the sense of Lebesgue measure) points with convergent Birkhoff averages. In particular, the time average of atomic measures along orbits of such points converges to some Sinai-Ruelle-Bowen-like measure in the weak* topology. Moreover, such points carry zero entropy. In contrast, irregular points are non-observable but carry infinite entropy.
2018

### Properties of invariant measures in dynamical systems with the shadowing property

#### Ergodic Theory and Dynamical Systems

38(6) (2018), 2257-2294.

Journal Paper J. Li, P. Oprocha

### Properties of invariant measures in dynamical systems with the shadowing property

J. Li, P. Oprocha
Journal Paper
For dynamical systems with the shadowing property, we provide a method of approximation of invariant measures by ergodic measures supported on odometers and their almost one-to-one extensions. For a topologically transitive system with the shadowing property, we show that ergodic measures supported on odometers are dense in the space of invariant measures, and then ergodic measures are generic in the space of invariant measures. We also show that for every and the collection of ergodic measures (supported on almost one-to-one extensions of odometers) with entropy between and is dense in the space of invariant measures with entropy at least . Moreover, if in addition the entropy function is upper semi-continuous, then, for every , ergodic measures with entropy are generic in the space of invariant measures with entropy at least c.
2018

### Ultrafilters and Ramsey-type shadowing phenomena in topological dynamics

#### Israel Journal of Mathematics

227 (2018), 423–453.

Journal Paper W. Brian, P. Oprocha

### Ultrafilters and Ramsey-type shadowing phenomena in topological dynamics

W. Brian, P. Oprocha
Journal Paper
We explore five variants of the Ramsey shadowing property. Each variant is a different way of formalizing the notion that, in a given dynamical system, every sequence of points looks like an orbit. The main goal is to relate these properties to more classical notions in topological dynamics.
2018

### Edrei’s Conjecture Revisited

#### Annales Henri Poincaré

19 (2018), 267–281.

Journal Paper J. P. Boronski, J. Kupka, P. Oprocha

### Edrei’s Conjecture Revisited

J. P. Boronski, J. Kupka, P. Oprocha
Journal Paper
Motivated by a recent result of Ciesielski and Jasiński we study periodic point free Cantor systems that are conjugate to systems with vanishing derivative everywhere, and more generally locally radially shrinking maps. Our study uncovers a whole spectrum of dynamical behaviors attainable for such systems, providing new counterexamples to the Conjecture of Edrei from 1952, first disproved by Williams in 1954.
2018

### Corrigendum to “Syndetically proximal pairs” [J. Math. Anal. Appl. 379 (2011) 656–663]

#### Journal of Mathematical Analysis and Applications

459(1) (2018), 614-617.

Journal Paper J. Li, .K. Subrahmonian Moothathu, P. Oprocha

### Corrigendum to “Syndetically proximal pairs” [J. Math. Anal. Appl. 379 (2011) 656–663]

J. Li, .K. Subrahmonian Moothathu, P. Oprocha
Journal Paper
We give a counterexample to Theorem 9 in “Syndetically proximal pairs” [J. Math. Anal. Appl. 379 (2011) 656–663]. We also provide sufficient conditions for the conclusion of Theorem 9 to hold.
2022

### On dynamics of the Sierpinski carpet

#### Comptes Rendus Mathematique

356(3) (2018), 340-344.

Journal Paper J.P. Boronski, P. Oprocha

### On dynamics of the Sierpinski carpet

J.P. Boronski, P. Oprocha
Journal Paper
We prove that the Sierpinski curve admits a homeomorphism with strong mixing properties. We also prove that the constructed example does not have Bowen’s specification property.
2018

### Failures prediction based on performance monitoring of a gas turbine: a binary classification approach

#### Schedae Informaticae

26 (2018), article id: 10832.

Journal Paper B. Mulewicz, M. Marzec, P. Morkisz, P. Oprocha

### Failures prediction based on performance monitoring of a gas turbine: a binary classification approach

B. Mulewicz, M. Marzec, P. Morkisz, P. Oprocha
Journal Paper
This paper is dedicated to employ novel technique of deep learning for machines failures prediction. General idea of how to transform sensor data into suitable data set for prediction is presented. Then, neural network architecture that is very successful in solving such problems is derived. Finally, we present a case study for real industrial data of a gas turbine, including results of the experiments.
2018

### An attempt of optimization of zinc production line

#### Archives of Civil and Mechanical Engineering

18(4) (2018), 1116-1122.

Journal Paper P. Jarosz, J. Kusiak, S. Małecki, P. Morkisz, P. Oprocha, W. Piertucha and Ł. Sztangret

### An attempt of optimization of zinc production line

P. Jarosz, J. Kusiak, S. Małecki, P. Morkisz, P. Oprocha, W. Piertucha and Ł. Sztangret
Journal Paper
The goal of the research is an attempt of optimization of the hydrometallurgy-based zinc production line, consisting of three stages: mixing of raw materials, oxidative roasting and leaching. The output product of one stage is an input to the next stage. Goal of mixing is preparation of zinc concentrates mix on the basis of zinc concentrates originated from different mines. The output semi-product of the next stage, the oxidative roasting process, is calcine, which is the input of the leaching. The result of the leaching is zinc sulfate solution and the goal of leaching is to carry out the maximum amount of zinc to solution. The preliminary step of any optimization is modeling of the analyzed processes. Modeling of considered three stages of zinc production line, based on the real industrial data of one of zinc production plants, was performed using different techniques. The elaborated models were the basis of the optimization for given objective functions of each of the production stages. The optimization methodology of multi-stage processes developed by the authors was applied. Obtained results of modeling and optimization are presented
2018

### Shadowing, Entropy and Minimal Sets

#### Springer Proceedings in Mathematics & Statistics

In: Dynamical Systems in Theoretical Perspective
Springer Proceedings in Mathematics & Statistics, vol. 248
pp. 249-259

Conference proceedings P. Oprocha

### Shadowing, Entropy and Minimal Sets

P. Oprocha
Conference proceedings
In this review paper we describe some consequences of the shadowing property for global and local aspects of dynamics. We will put additional emphasis on approximation of invariant measures by er- godic measures with additional properties of their supports (minimality, positive entropy, mixing).
2017

### On dynamics of graph maps with zero topological entropy

#### Nonlinearity

30 (2017), article id: 4260.

Journal Paper J. Li, P. Oprocha, Y. Yang, T. Zeng

### On dynamics of graph maps with zero topological entropy

J. Li, P. Oprocha, Y. Yang, T. Zeng
Journal Paper
We explore the dynamics of graph maps with zero topological entropy. It is shown that a continuous map f on a topological graph G has zero topological entropy if and only if it is locally mean equicontinuous, that is the dynamics on each orbit closure is mean equicontinuous. As an application, we show that Sarnak’s Möbius disjointness conjecture is true for graph maps with zero topological entropy. We also extend several results known in interval dynamics to graph maps. We show that a graph map has zero topological entropy if and only if there is no 3-scrambled tuple if and only if the proximal relation is an equivalence relation; a graph map has no scrambled pairs if and only if it is null if and only if it is tame.
2017

### Validation of optimization strategies using the linear structured production chains

#### AIP Conference Proceedings

AIP Conference Proceedings, vol. 1836
Article id: 020067

Conference proceedings J. Kusiak, P. Morkisz, P. Oprocha, W. Pietrucha, Ł. Sztangret

### Validation of optimization strategies using the linear structured production chains

J. Kusiak, P. Morkisz, P. Oprocha, W. Pietrucha, Ł. Sztangret
Conference proceedings
Different optimization strategies applied to sequence of several stages of production chains were validated in this paper. Two benchmark problems described by ordinary differential equations (ODEs) were considered. A water tank and a passive CR-RC filter were used as the exemplary objects described by the first and the second order differential equations, respectively. Considered in the work optimization problems serve as the validators of strategies elaborated by the Authors. However, the main goal of research is selection of the best strategy for optimization of two real metallurgical processes which will be investigated in an on-going projects. The first problem will be the oxidizing roasting process of zinc sulphide concentrate where the sulphur from the input concentrate should be eliminated and the minimal concentration of sulphide sulphur in the roasted products has to be achieved. Second problem will be the lead refining process consisting of three stages: roasting to the oxide, oxide reduction to metal and the oxidizing refining. Strategies, which appear the most effective in considered benchmark problems will be candidates for optimization of the mentioned above industrial processes.
2016

### Multi-criteria optimization strategies for production chains

#### MATEC Web of Confonferences

MATEC Web of Conferences, vol. 80
Article id: 10008

Conference proceedings J. Kusiak, P. Morkisz, P. Oprocha, W. Pietrucha, Ł. Sztangret

### Multi-criteria optimization strategies for production chains

J. Kusiak, P. Morkisz, P. Oprocha, W. Pietrucha, Ł. Sztangret
Conference proceedings
The aim of this paper is presentation of some optimization strategies applicable in the optimization of multi-stage and multi-threads chain structures (linear or tree-structured, acyclic graphs) with multiple intermediate goal functions. The inspirations for this type of analysis are production chains often seen in industrial plants. Production in these plants consists of sequences of multiple units connected linearly or in tree which, at various production stages, intermediate quality criteria, related to the semi-products, may occur.
2014

### On a Cipher Based on Pseudo-random Walks on Graphs

#### Communications in Computer and Information Science,

In: Cryptography and Security Systems
Communications in Computer and Information Science, vol. 448
pp. 59-73.

Conference proceedings W. Foryś, Ł. Jęda, P. Oprocha

### On a Cipher Based on Pseudo-random Walks on Graphs

W. Foryś, Ł. Jęda, P. Oprocha
Conference proceedings
In the paper a cipher which uses transition graph in the encryption and decryption processes is presented. It is created based on some ideas of dynamic systems (symbolic dynamics). The introduced cipher is tested according to the suggestions of FIPS 140-2 standard and the results are presented in the paper.
2014

### Topological aspects of dynamics of pairs, tuples and sets

#### Atlantis Press

Recent Progress in General Topology III
K.P. Hart, J. van Mill, P. Simon (Eds.)
Atlantis Press, 2014, pp. 649-692.

Book Chapter P. Oprocha, G.H. Zhang

### Topological aspects of dynamics of pairs, tuples and sets

P. Oprocha, G.H. Zhang
Book Chapter
The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.
2009

### Optimization: Selected methods and their applications

#### Polish Scientific Publishers PWN

Warsaw, 2009

Book J. Kusiak, A. Danielewska-Tułecka, P. Oprocha

### Optimization: Selected methods and their applications

J. Kusiak, A. Danielewska-Tułecka, P. Oprocha
Book
.05

## POSITIONS

CURRENT
• 2018
NOW
Kraków

### Full Professor

#### AGH University of Science and Technology

Faculty of Applied Mathematics
PREVIOUS
• 2020
2022
Kraków, Poland

### Dean

#### AGH University of Science and Technology

Faculty of Applied Mathematics
• 2020
2012
Kraków, Poland

### Deputy Dean for Science

#### AGH University of Science and Technology

Faculty of Applied Mathematics
• 2018
2012
Kraków, Poland

### Associate Professor

#### AGH University of Science and Technology

Faculty of Applied Mathematics
• 2012
2006
Kraków, Poland

#### AGH University of Science and Technology

Faculty of Applied Mathematics
• 2006
2002
Kraków, Poland

### ASSISTANT PROFESSOR

#### AGH University of Science and Technology

Faculty of Applied Mathematics
.06

## Conferences

Forthcoming conferences
Past conferences
• Sęp
2022
Gdańsk, Poland

### On the Trail of Women in Mathematics - Contemporary Women in Mathematics

#### Gdańsk University of Technology

Talk: On pseudoarc and dynamics

• Jul
2022
Prague, Czech Republic

### Prague Symposia on General Topology (Toposym 2022)

#### Charles University

Talk: On pseudoarc and dynamics

• Jul
2022
Paris-Saclay, France

### 27th International Conference on Difference Equations and Applications (ICDEA 2022)

#### Universite Paris-Saclay

Talk: On typical properties of Lebesgue measure preserving maps in dimension one

• Apr
2022
Będlewo, Poland

### Inspirations in Real Analysis

#### Banach Center

Talk: On typical properties of Lebesgue measure preserving maps in dimension one

• Jan
2022
Cullera, Spain

### Recent Trends in Nonlinear Science (18th RTNS)

#### Universitat Politècnica de Valencia

Winter school in Dynamical Systems of the DANCE (Dinámica, Atractores y Nolinealidad: Caos y Estabilidad) Spanish network.

Course: Tracing, mixing and entropy

• Dec
2021
Łódź, Poland

### Dynamical Systems Theory and Applications (DSTA 2021)

#### Lodz University of Technology

Talk: On dynamics of Lorenz maps

• Jul
2021
Moscow, Russia

### Mathematical Physics, Dynamical Systems and Infinite-Dimensional Analysis – 2021

#### Steklov International Mathematical Center

Talk: On typical properties of Lebesgue measure preserving maps in dimension one.

• Jun
2021
Portorož, Slovenia

### 8th European Congress of Mathematics

#### University of Primorska

Talk: Zero topological entropy and invariant measures in dimension one

• Jun
2021
Prague, Czech Republic

### The 9th Visegrad Conference Dynamical Systems,

#### Czech Technical University in Prague

Talk: On typical properties of Lebesgue measure preserving maps in dimension one

• May
2021
Murray, KY, USA

### The 54th Spring Topology and Dynamical Systems Conference

#### Murray State University

Talk: On completely invariant sets in Lorenz maps

• Apr
2021
Barcelona, Spain

### Workshop on Topological and Combinatorial Dynamics

#### Centre de Recerca Matematica

Talk: On dynamics of Lorenz maps

• Jul
2019
Łódź, Poland

### Dynamics of (Semi-)Group Actions

#### University of Łódź

Talk: On the entropy conjecture of Marcy Barge

• Jun
2019
Dubrovnik, Croatia

### Dubrovnik IX - Topology & Dynamical System

#### Inter-University Centre Dubrovnik

Talk: On the entropy conjecture of Marcy Barge

.07

## CONTACT

Faculty of Applied Mathematics
AGH University of Science and Technology
al. Mickiewicza 30
30-059 Kraków, Poland

### e-mail

oprocha(at)agh.edu.pl

### office

Building A4
Office 117 (1st floor)