On the hyperbolicity of homoclinic classes

Abstract

We give a sufficient criterion for the hyperbolicity of a homoclinic class. More precisely, if the homoclinic class H(p) admits a partially hyperbolic splitting TH(p)M = Es ⊕lt; F, where Es is uniformly contracting and dimEs = ind(p), and all periodic points homoclinically related with p are uniformly E u-expanding at the period, then H(p) is hyperbolic. We also give some consequences of this result.