Equilibrium states for partially hyperbolic diffeomorphisms with hyperbolic linear part

TL;DR

This paper investigates the existence and uniqueness of ergodic equilibrium states for a class of partially hyperbolic diffeomorphisms homotopic to Anosov, using disintegration along central foliation.

Contribution

It introduces a novel approach of studying equilibrium states via disintegration along central foliation for partially hyperbolic systems.

Findings

Established conditions for existence of equilibrium states

Proved uniqueness and finiteness of these states under certain conditions

Developed a new framework for analyzing equilibrium states in partially hyperbolic dynamics

Abstract

We address the problem of existence and uniqueness (finite- ness) of ergodic equilibrium states for a natural class of partially hyperbolic dynamics homotopic to Anosov. We propose to study the disintegration of equilibrium states along central foliation as a tool to develop the theory of equilibrium states for partially hyperbolic dynamics.