Equilibrium states for maps isotopic to Anosov

TL;DR

This paper investigates the existence and uniqueness of ergodic equilibrium states for certain partially hyperbolic diffeomorphisms on the 4-torus, using measure disintegration techniques along center foliation subbundles.

Contribution

It introduces a novel approach to analyze measure disintegration along subfoliations for maps isotopic to Anosov, providing new characterizations of ergodic measures.

Findings

Existence and finiteness of equilibrium states established.

Disintegration of measures along 1-dimensional subfoliations characterized.

General results on measure disintegration in this context obtained.

Abstract

In this work we address the problem of existence and uniqueness (finiteness) of ergodic equilibrium states for partially hyperbolic diffeomorphisms isotopic to Anosov on $\mathbb{T}^4$, with 2-dimensional center foliation. To do so we propose to study the disintegration of measures along 1-dimensional subfoliations of the center bundle. Moreover, we obtain a more general result characterizing the disintegration of ergodic measures in our context.