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arXiv · 1710.08487

On the F-expanding of Homoclinic class

Wanlou Wu·Bo Li
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Abstract

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

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Wanlou Wu, Bo Li. 2017-10-23. On the F-expanding of Homoclinic class. https://arxiv.org/abs/1710.08487

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