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

Michael Hochman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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 languageAmerican English
Pages (from-to)271-317
Number of pages47
JournalJournal of the European Mathematical Society
Volume21
Issue number1
DOIs
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© European Mathematical Society 2019.

Keywords

  • Borel dynamics
  • Entropy
  • Ergodic theory
  • Generators

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