63 citations · 230 across the 33 of their papers we have counts for
38 papers
The conjugacy and flip conjugacy problem for Cantor minimal systems
Konrad Deka, Kosma Kasprzak, Philipp Kunde +2
We prove that topological conjugacy and flip conjugacy of minimal homeomorphisms of a Cantor space are complete analytic relations and hence are not Borel. We also prove that mutua…
Spectrum of invariant measures via generic points
Sejal Babel, Melih Emin Can, Dominik Kwietniak +1
We describe the spectrum of an ergodic invariant measure by examining the behaviour of its generic points. We define regular Wiener--Wintner generic points for a measure to general…
On mixing and dense periodicity on spaces with a free arc
Dominik Kwietniak, Filip Wierzbowski
We study the dynamics of continuous maps on compact metric spaces containing a free interval (an open subset homeomorphic to the interval ). We provide a new proof of a resu…
On entropy of pure mixing maps on dendrites
Dominik Kwietniak, Piotr Oprocha, Jakub Tomaszewski
For every we construct a continuous pure mixing map (topologically mixing, but not exact) on the Gehman dendrite with topological entropy . It has been previously…
Equilibrium states by synchronization, symbolic extensions, and factors
Katrin Gelfert, Dominik Kwietniak, Yuri Lima
We combine the two classical topological concepts, time-preserving topological factors and synchronizing time-changes of a continuous flow, and explore some of their thermodynamic…
A note on logarithmic mean equicontinuity
Dominik Kwietniak, Jian Li, Habibeh Pourmand
We study the set of harmonic limits of empirical measures in topological dynamical systems. We obtain a characterization of unique ergodicity based of logarithmic (harmonic) mean c…
Even the vague specification property implies density of ergodic measures
Damla Buldağ, Bhishan Jacelon, Dominik Kwietniak
We prove that if a topological dynamical system is surjective and has the vague specification property, then its ergodic measures are dense in the space of all invariant me…
Automorphism groups of measures on the Cantor space. Part I: Good measures and Rokhlin properties
Michal Doucha, Dominik Kwietniak, Maciej Malicki +1
We study criteria for the existence of a dense or comeager conjugacy class in the automorphism group of a given measure on the Cantor space. We concentrate on good measures, define…
Bowen's Problem 32 and the conjugacy problem for systems with specification
Konrad Deka, Dominik Kwietniak, Bo Peng +1
We show that Rufus Bowen's Problem 32 on the classification of symbolic systems with the specification property does not admit a solution that would use concrete invariants. To thi…
Minimal and proximal examples of -stable and -approachable shift spaces
Melih Emin Can, Jakub Konieczny, Michal Kupsa +1
We study shift spaces over a finite alphabet that can be approximated by mixing shifts of finite type in the sense of (pseudo)metrics connected to Ornstein's metric ($\ba…
The descriptive complexity of the set of Poisson generic numbers
Verónica Becher, Stephen Jackson, Dominik Kwietniak +1
Let be an integer. We show that the set of real numbers that are Poisson generic in base is -complete in the Borel hierarchy of subsets of the real l…
On the properties of the mean orbital pseudo-metric
Fangzhou Cai, Dominik Kwietniak, Jian Li +1
Given a topological dynamical system , we study properties of the mean orbital pseudo-metric defined by \[ \bar E(x,y)= \limsup_{n\to\infty } \min_{σ\in S_n}\frac{1…
Borel complexity of sets of points with prescribed Birkhoff averages in Polish dynamical systems with a specification property
Konrad Deka, Steve Jackson, Dominik Kwietniak +1
We study the descriptive complexity of sets of points defined by placing restrictions on statistical behaviour of their orbits in dynamical systems on Polish spaces. A particular e…
On -approachability, entropy density and -free shifts
Jakub Konieczny, Michal Kupsa, Dominik Kwietniak
We study approximation schemes for shift spaces over a finite alphabet using (pseudo)metrics connected to Ornstein's metric. This leads to a class of shift spaces we call…
Amorphic complexity of group actions with applications to quasicrystals
Gabriel Fuhrmann, Maik Gröger, Tobias Jäger +1
In this article, we define amorphic complexity for actions of locally compact -compact amenable groups on compact metric spaces. Amorphic complexity, originally introduced for $…
Uniform continuity of entropy rate with respect to the -pseudometric
Tomasz Downarowicz, Dominik Kwietniak, Martha Łącka
Assume that a sequence is frequency-typical for a finite-valued stationary stochastic process . We prove that the function associating to the entrop…
On topological models of zero entropy loosely Bernoulli systems
Felipe García-Ramos, Dominik Kwietniak
We provide a purely topological characterisation of uniquely ergodic topological dynamical systems (TDSs) whose unique invariant measure is zero entropy loosely Bernoulli (followin…
On tameness of almost automorphic dynamical systems for general groups
Gabriel Fuhrmann, Dominik Kwietniak
Let be a minimal equicontinuous dynamical system, where is a compact metric space and some topological group acting on . Under very mild assumptions, we show tha…
Borel complexity of sets of normal numbers via generic points in subshifts with specification
Dylan Airey, Steve Jackson, Dominik Kwietniak +1
We study the Borel complexity of sets of normal numbers in several numeration systems. Taking a dynamical point of view, we offer a unified treatment for continued fraction expansi…
Robust existence of nonhyperbolic ergodic measures with positive entropy and full support
Christian Bonatti, Lorenzo J. Díaz, Dominik Kwietniak
We prove that for some manifolds the set of robustly transitive partially hyperbolic diffeomorphisms of with one-dimensional nonhyperbolic centre direction contains a …
Sarnak's conjecture implies the Chowla conjecture along a subsequence
Alexander Gomilko, Dominik Kwietniak, Mariusz Lemańczyk
We show that the Möbius disjointess of zero entropy dynamical systems implies the existence of an increasing sequence of positive integers along which the Chowla conjecture on auto…
Feldman-Katok pseudometric and the GIKN construction of nonhyperbolic ergodic measures
Dominik Kwietniak, Martha Łącka
The GIKN construction was introduced by Gorodetski, Ilyashenko, Kleptsyn, and Nalsky in [Functional Analysis and its Applications, 39 (2005), 21--30]. It gives a nonhyperbolic ergo…
Arcwise connectedness of the set of ergodic measures of hereditary shifts
Jakub Konieczny, Michal Kupsa, Dominik Kwietniak
We show that the set of ergodic invariant measures of a shift space with a safe symbol (this includes all hereditary shifts) is arcwise connected when endowed with the -bar metr…
Generic Points for Dynamical Systems with Average Shadowing
Dominik Kwietniak, Martha Łącka, Piotr Oprocha
It is proved that to every invariant measure of a compact dynamical system one can associate a certain asymptotic pseudo orbit such that any point asymptotically tracing in average…