Equilibrium states for certain partially hyperbolic attractors

TL;DR

This paper establishes the uniqueness of equilibrium states for a class of partially hyperbolic attractors, especially under smoothness and foliation conditions, using advanced thermodynamic formalism techniques.

Contribution

It extends the theory of equilibrium states to certain partially hyperbolic attractors with invariant foliations, applying new techniques to prove uniqueness.

Findings

Unique equilibrium states for the class of attractors introduced by Castro and Nascimento.

Existence of a unique equilibrium state for the geometric potential in smooth cases.

Application of Climenhaga and Thompson's methods to partially hyperbolic dynamics.

Abstract

We prove that a class of partially hyperbolic attractors introduced by Castro and Nascimento have unique equilibrium states for natural classes of potentials. We also show if the attractors are $C^2$ and have invariant stable and centerunstable foliations, then there is a unique equilibrium state for the geometric potential and its 1-parameter family. We do this by applying general techniques developed by Climenhaga and Thompson.