Equilibrium States for Center Isometries

TL;DR

This paper introduces a geometric approach to prove existence and uniqueness of equilibrium states for center isometries, including entropy-maximizing and SRB measures, and characterizes these states via foliation disintegrations, showing Bernoulli isomorphism.

Contribution

It provides a novel geometric method to establish equilibrium states for center isometries, extending understanding of their measure-theoretic properties.

Findings

Existence and uniqueness of equilibrium states proven for certain potentials.

Characterization of equilibrium states via disintegrations along foliations.

System shown to be isomorphic to a Bernoulli scheme.

Abstract

We develop a geometric method to establish existence and uniqueness of equilibrium states associated to some H\"older potentials for center isometries (as are regular elements of Anosov actions), in particular the entropy maximizing measure and the SRB measure. It is also given a characterization of equilibrium states in terms of their disintegrations along stable and unstable foliations. Finally, we show that the resulting system is isomorphic to a Bernoulli scheme.