Every Borel automorphism without finite invariant measures admits a two-set generator

Michael Hochman

doi:10.4171/JEMS/836

Every Borel automorphism without finite invariant measures admits a two-set generator

Michael Hochman

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

We show that if an automorphism of a standard Borel space does not admit finite invariant measures, then it has a two-set generator. This implies that if the entropies of invariant probability measures of a Borel system are all less than log k, then the system admits a k-set generator, and that a wide class of hyperbolic-like systems are classified completely at the Borel level by entropy and periodic points counts.

Original language	English
Pages (from-to)	271-317
Number of pages	47
Journal	Journal of the European Mathematical Society
Volume	21
Issue number	1
DOIs	https://doi.org/10.4171/JEMS/836
State	Published - 2019

Keywords

Borel dynamics
Entropy
Ergodic theory
Generators

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.4171/JEMS/836

Cite this

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abstract = "We show that if an automorphism of a standard Borel space does not admit finite invariant measures, then it has a two-set generator. This implies that if the entropies of invariant probability measures of a Borel system are all less than log k, then the system admits a k-set generator, and that a wide class of hyperbolic-like systems are classified completely at the Borel level by entropy and periodic points counts.",

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AB - We show that if an automorphism of a standard Borel space does not admit finite invariant measures, then it has a two-set generator. This implies that if the entropies of invariant probability measures of a Borel system are all less than log k, then the system admits a k-set generator, and that a wide class of hyperbolic-like systems are classified completely at the Borel level by entropy and periodic points counts.

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KW - Ergodic theory

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Every Borel automorphism without finite invariant measures admits a two-set generator

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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