Gibbs measures have local product structure
Dynamical Systems
2025-04-04 v2
Abstract
It is well-known that equilibrium measures for uniformly hyperbolic dynamical systems have a local product structure, which plays an important role in their mixing properties. Existing proofs of this fact rely either on transfer operators or on leafwise constructions, and in particular are not well-suited to the approach to thermodynamic formalism based on Bowen's specification property. Here we provide an alternate proof based on the Gibbs property, which fits more comfortably in that approach.
Cite
@article{arxiv.2310.17495,
title = {Gibbs measures have local product structure},
author = {Vaughn Climenhaga},
journal= {arXiv preprint arXiv:2310.17495},
year = {2025}
}
Comments
13 pages. In v1, the passage following the statement of Proposition 5.4 contained an error; this is avoided in v2 by modifying the proof of the main result