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

  • Michael Hochman

    The Hebrew University of Jerusalem, Israel
Every Borel automorphism without finite invariant measures admits a two-set generator cover

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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 , then the system admits a -set generator, and that a wide class of hyperbolic-like systems are classified completely at the Borel level by entropy and periodic points counts.

Cite this article

Michael Hochman, Every Borel automorphism without finite invariant measures admits a two-set generator. J. Eur. Math. Soc. 21 (2019), no. 1, pp. 271–317

DOI 10.4171/JEMS/836