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arXiv · 1810.08663

Equilibrium measures for some partially hyperbolic systems

Vaughn Climenhaga·Yakov Pesin·Agnieszka Zelerowicz
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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.

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Vaughn Climenhaga, Yakov Pesin, Agnieszka Zelerowicz. 2018-10-19. Equilibrium measures for some partially hyperbolic systems. https://doi.org/10.3934/jmd.2020006

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