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

2015/08/10 by Hochman, Michael
#28D20 #37A35 #37A40 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1508.02335

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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