Equilibrium measures for some partially hyperbolic systems

Vaughn Climenhaga, Yakov Pesin, Agnieszka Zelerowicz

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)155-205
Number of pages51
JournalJournal of Modern Dynamics
Volume16
DOIs
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Equilibrium measures for some partially hyperbolic systems'. Together they form a unique fingerprint.

Cite this