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arXiv · 2406.13004

Residuality of Dynamical Morphisms for Amenable Group Actions

Dawid Huczek·Sebastian Kopacz·Jacek Serafin
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Abstract

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, applying a similar reasoning to the case of actions of countably infinite amenable groups. In principle we follow the lines of the paper by Burton, Keane and Serafin (\cite{BKS}), showing that measures defining homomorphisms or isomorphisms form residual subsets in suitably chosen spaces of joinings.

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Dawid Huczek, Sebastian Kopacz, Jacek Serafin. 2024-06-18. Residuality of Dynamical Morphisms for Amenable Group Actions. https://arxiv.org/abs/2406.13004

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