Equilibrium measures for some partially hyperbolic systems
Abstract
We study thermodynamic formalism for topologically transitive partially hyperbolic systems in which the center-stable bundle satisfies a bounded expansion property, and show that every potential function satisfying the Bowen property has a unique equilibrium measure. Our method is to use tools from geometric measure theory to construct a suitable family of reference measures on unstable leaves as a dynamical analogue of Hausdorff measure, and then show that the averaged pushforwards of these measures converge to a measure that has the Gibbs property and is the unique equilibrium measure.
Cite
@article{arxiv.1810.08663,
title = {Equilibrium measures for some partially hyperbolic systems},
author = {Vaughn Climenhaga and Yakov Pesin and Agnieszka Zelerowicz},
journal= {arXiv preprint arXiv:1810.08663},
year = {2020}
}
Comments
The published version of this paper contains an error in the proof of Lemma 6.6, which is corrected here (the lemma remains correct as stated). arXiv admin note: text overlap with arXiv:1803.10374