Strong Positive recurrence for potential and exponential mixing of equilibrium states of surface diffeomorphisms

TL;DR

This paper investigates the strong positive recurrence property for potentials in surface diffeomorphisms, establishing statistical properties like exponential decay of correlations and effective ergodicity for equilibrium states.

Contribution

It introduces new results on the recurrence and mixing properties of equilibrium states for surface diffeomorphisms with positive entropy.

Findings

Exponential decay of correlations for equilibrium states

Effective intrinsic ergodicity established

Strong positive recurrence property proven for a broad class of potentials

Abstract

In this paper, we study the strong positive recurrence property for a large class of potentials of $C^{\infty}$ surface diffeomorphisms with positive entropy. We establish several statistical properties of the corresponding equilibrium states, including exponential decay of correlations and effective intrinsic ergodicity.