SRB measures and homoclinic relation for Endomorphisms

TL;DR

This paper establishes an upper bound on the number of SRB measures of saddle type for local diffeomorphisms, linking it to the maximal size of sets of periodic points without homoclinic relations.

Contribution

It introduces a new upper bound relating SRB measures to periodic points without homoclinic relations for boundaryless manifolds.

Findings

Upper bound for SRB measures based on periodic points

Connection between homoclinic relations and SRB measures

Applicable to local diffeomorphisms on boundaryless manifolds

Abstract

In this paper we give an upper bound for the number of SRB measures of saddle type of local diffeomorphisms of boundaryless manifolds in terms of maximal cardinality of set of periodic points without any homoclinic relation.