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Compact families and typical entropy invariants of measure-preserving actions

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.

preprint2021arXivOpen access
Valery V. Ryzhikov
math.DS
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Valery V. Ryzhikov

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