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arXiv · 1508.02335

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

Michael Hochman
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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 modulo the sigma-ideal generated by wandering sets. 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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Michael Hochman. 2015-08-10. Every Borel automorphism without finite invariant measures admits a two-set generator. https://arxiv.org/abs/1508.02335

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