Compact families and typical entropy invariants of measure-preserving actions
Dynamical Systems
2021-02-12 v1
Abstract
For a compact set of actions, an invariant of Kushnirenko's entropy type is chosen in such a way that on this set it is equal to zero, but will be infinity for typical actions. As a consequence, we show that typical measure-preserving transformations are not isomorphic to geometric shape exchange transformations. This problem arose in connection with the result of Chaika and Davis about the atypical nature of IETs.
Keywords
Cite
@article{arxiv.2102.06187,
title = {Compact families and typical entropy invariants of measure-preserving actions},
author = {Valery V. Ryzhikov},
journal= {arXiv preprint arXiv:2102.06187},
year = {2021}
}
Comments
in Russian. The article is intended for Volume 82:1 of Proceedings of the Moscow Mathematical Society, dedicated to the 80th anniversaries of V.I. Oseledets and A.M. Stepin and the memory of A.M. Stepin, who left us in November 2020