ON THE <i>F</i>-EXPANDING OF HOMOCLINIC CLASSES

Abstract

We establish a closing property for thin trapped (see Definition 1.2) homoclinic classes. Taking advantage of this property, we prove that if a homoclinic class $H(f, p)$ admits a dominated splitting $T_{H(f, p)}M=E\oplus_{ < }F$, where the subbundle $E$ is thin trapped with dim$E=$Ind$(p)$ and all periodic points homoclinically related to $p$ are uniformly $F$-expanding at the period (see Definition 1.1), then the subbundle $F$ is uniformly expanding.