Every Borel automorphism without finite invariant measures admits a two-set generator
Dynamical Systems
2017-06-07 v2
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.
Keywords
Cite
@article{arxiv.1508.02335,
title = {Every Borel automorphism without finite invariant measures admits a two-set generator},
author = {Michael Hochman},
journal= {arXiv preprint arXiv:1508.02335},
year = {2017}
}
Comments
57 pages. v2: some corrections to proofs, statements unchanged