Equilibrium measures for some partially hyperbolic systems
Year: 2020
Type: article
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.
Source: Journal of Modern Dynamics
DOI: 10.3934/jmd.2020006
Authors: Vaughn Climenhaga, Yakov Pesin, Agnieszka Zelerowicz
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Brown University
OpenAlex ID: W2896479310