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.

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