Advanced Search
Article Contents
Article Contents

Minimal non-hyperbolicity and index-completeness

Abstract Related Papers Cited by
  • We study a problem raised by Abdenur et. al. [3] that asks, for any chain transitive set $\Lambda$ of a generic diffeomorphism $f$, whether the set $I(\Lambda)$ of indices of hyperbolic periodic orbits that approach $\Lambda$ in the Hausdorff metric must be an "interval", i.e., whether $\alpha\in I(\Lambda)$ and $\beta\in I(\Lambda)$, $\alpha<\beta$, must imply $\gamma\in I(\Lambda)$ for every $\alpha<\gamma<\beta$. We prove this is indeed the case if, in addition, $f$ is $C^1$ away from homoclinic tangencies and if $\Lambda$ is a minimally non-hyperbolic set.
    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


    \begin{equation} \\ \end{equation}
  • 加载中

Article Metrics

HTML views() PDF downloads(71) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint