Dominik Kwietniak
Jagiellonian University
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Publication
Featured researches published by Dominik Kwietniak.
Fundamenta Mathematicae | 2014
Marcin Kulczycki; Dominik Kwietniak; Piotr Oprocha
In this paper we study relations between almost specification property, asymptotic average shadowing property and average shadowing property for dynamical systems on compact metric spaces. We show implications between these properties and relate them to other important notions such as shadowing, transitivity, invariant measures, etc. We provide examples that compactness is a necessary condition for these implications to hold. As a consequence of our methodology we also obtain a proof that limit shadowing in chain transitive systems implies shadowing.
Qualitative Theory of Dynamical Systems | 2005
Dominik Kwietniak; Michał Misiurewicz
We modify the definition of chaos in the sense of Devaney, by replacing the condition of topological transitivity by topological exactness. We study basic properties of exact Devaney chaos defined in such a way. We also investigate the infimum of topological entropies of exactly Devaney chaotic maps of a given space.
Journal of Difference Equations and Applications | 2011
Grzegorz Harańczyk; Dominik Kwietniak; Piotr Oprocha
Two elementary proofs showing that (i) transitivity and sensitivity imply dense periodicity for maps on topological graphs and (ii) total transitivity and dense periodicity imply mixing for maps on spaces with an open subset homeomorphic with the open interval (0,1) are presented. As corollaries, one gets new and simple proofs that Auslander–Yorke chaos implies Devaney chaos, and weak mixing implies mixing for graph maps.
Proceedings of the American Mathematical Society | 2008
Grzegorz Harańczyk; Dominik Kwietniak
It is proved that the infimum of the topological entropy of continuous topologically exact interval (circle) maps is strictly smaller than the infimum of the topological entropy of continuous interval (circle) maps, which are topologically mixing, but not exact. Interpreting this result in terms of popular notions of chaos, one may say that on the interval (circle) lower entropy implies stronger Devaney chaos. Moreover, the infimum of the entropy of mixing circle maps is computed. These theorems may be considered as a completion of some results of Alseda, Kolyada, Llibre, and Snoha (1999).
Science China-mathematics | 2017
Dominik Kwietniak; Jian Li; Piotr Oprocha; Xiangdong Ye
We explore recurrence properties arising from dynamical approach to the van der Waerden theorem and similar combinatorial problems. We describe relations between these properties and study their consequences for dynamics. In particular, we present a measure-theoretical analog of a result of Glasner on multi-transitivity of topologically weakly mixing minimal maps. We also obtain a dynamical proof of the existence of a C-set with zero Banach density.
Monatshefte für Mathematik | 2017
Dominik Kwietniak; Martha Łącka; Piotr Oprocha
We study the Besicovitch pseudometric
Dynamical Systems-an International Journal | 2013
Dominik Kwietniak; Martha Ubik
Dynamical Systems-an International Journal | 2012
Marcin Kulczycki; Dominik Kwietniak
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American Mathematical Monthly | 2018
Marcin Kulczycki; Dominik Kwietniak; Jian Li
Ergodic Theory and Dynamical Systems | 2017
Jakub Byszewski; Fryderyk Falniowski; Dominik Kwietniak
DB for compact dynamical systems. The set of generic points of ergodic measures turns out to be closed with respect to