Uniqueness of SRB measures for transitive diffeomorphisms on surfaces

TL;DR

This paper proves that transitive surface diffeomorphisms have at most one SRB measure and describes ergodic components using homoclinic classes, advancing understanding of statistical properties of dynamical systems.

Contribution

It establishes the uniqueness of SRB measures for transitive surface diffeomorphisms and characterizes ergodic components via homoclinic classes, providing new insights into their structure.

Findings

At most one SRB measure exists for transitive surface diffeomorphisms

Ergodic components are described in terms of homoclinic classes

Provides a framework linking hyperbolic periodic points to SRB measures

Abstract

We give a description of ergodic components of SRB measures in terms of ergodic homoclinic classes associated to hyperbolic periodic points. For transitive surface diffeomorphisms, we prove that there exists at most one SRB measure.