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 σ-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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