30 citations · 45 across the 10 of their papers we have counts for
12 papers
Residuality of Dynamical Morphisms for Amenable Group Actions
Dawid Huczek, Sebastian Kopacz, Jacek Serafin
We extend the classical Baire category approach, used in proving the finite generator theorem of Krieger, the homomorphism theorem of Sinai and the isomorphism theorem of Ornstein,…
Factoring strongly irreducible group shift actions onto full shifts of lower entropy
Dawid Huczek, Sebastian Kopacz
We show that if is a a countable amenable group with the comparison property, and is a strongly irreducible -shift satisfying certain aperiodicity conditions, then f…
Empirical approach to the x2, x3 conjecture
Tomasz Downarowicz, Dawid Huczek
We study atomic measures on which are invariant both under multiplication by and by , since such measures play an important role in deciding Furstenberg'…
A comment on ergodic theorem for amenable groups
Bartosz Frej, Dawid Huczek
We prove a version of ergodic theorem for an action of an amenable group, where a Fø lner sequence needs not to be tempered. Instead, it is assumed that a function satisfies certai…
Extensions of Full Shifts with Group Actions
Bartosz Frej, Dawid Huczek
We give a sufficient condition for a symbolic topological dynamical system with action of a countable amenable group to be an extension of the full shift, a problem analogous to th…
Doubly stochastic operators with zero entropy
Bartosz Frej, Dawid Huczek
We study doubly stochastic operators with zero entropy. We generalize three famous theorems: the Rokhlin's theorem on genericity of zero entropy, the Kushnirenko's theorem on equiv…
Dynamical quasitilings of amenable group
Tomasz Downarowicz, Dawid Huczek
We prove that for any compact zero-dimensional metric space on which an infinite countable amenable group acts freely by homeomorphisms, there exists a dynamical quasitilin…
Faces of simplices of invariant measures for actions of amenable groups
Bartosz Frej, Dawid Huczek
We prove that every face in the simplex of invariant measures on a zero-dimensional dynamical system with free action of an amenable group can be modeled as the entire simplex…
Zero-dimensional extensions of amenable group actions
Dawid Huczek
We prove that every dynamical system with free action of a countable amenable group by homeomorphisms has a zero-dimensional extension which is faithful and principal,…
Tilings of amenable groups
Tomasz Downarowicz, Dawid Huczek, Guohua Zhang
We prove that for any infinite countable amenable group , any and any finite subset , there exists a tiling (partition of into finite "tiles" using only f…
Minimal models for actions of amenable groups
Bartosz Frej, Dawid Huczek
We prove that on a metrizable, compact, zero-dimensional space every free action of an amenable group is measurably isomorphic to a minimal -action with the same, i.e. affinely…
Rank as a function of measure
Tomasz Downarowicz, Yonatan Gutman, Dawid Huczek
We establish certain topological properties of rank understood as a function on the set of invariant measures on a topological dynamical system. To be exact, we show that rank is o…