\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

$C^1$ -stably weakly shadowing homoclinic classes admit dominated splittings

Abstract Related Papers Cited by
  • Let $f$ be a diffeomorphism of a closed $n$-dimensional $C^\infty$ manifold, and $p$ be a hyperbolic saddle periodic point of $f$. In this paper, we introduce the notion of $C^1$-stably weakly shadowing for a closed $f$-invariant set, and prove that for the homoclinic class $H_f(p)$ of $p$, if $f_{|H_f(p)}$ is $C^1$-stably weakly shadowing, then $H_f(p)$ admits a dominated splitting. Especially, on a 3-dimensional manifold, the splitting on $H_f(p)$ is partially hyperbolic, and if in addition, $f$ is far from homoclinic tangency, then $H_f(p)$ is strongly partially hyperbolic.
    Mathematics Subject Classification: Primary: 37B20, 37C29, 37C50, 37D20, 37D30.

    Citation:

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

Article Metrics

HTML views() PDF downloads(96) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return