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math.DS2024
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,…
math.DS2014★ 3 cited
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…
math.DS2012
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…