Advanced Search
Article Contents
Article Contents

Transversality properties and $C^1$-open sets of diffeomorphisms with weak shadowing

Abstract Related Papers Cited by
  • Let Int$^1WS(M)$ be the $C^1$-interior of the set of diffeomorphisms of a smooth closed manifold $M$ having the weak shadowing property. The second author has shown that if $\dim M = 2$ and all of the sources and sinks of a diffeomorphism $f \in$ Int$^1WS(M)$ are trivial, then $f$ is structurally stable. In this paper, we show that there exist diffeomorphisms $f \in$ Int$^1WS(M)$, $\dim M = 2$, such that $(i)$ $f$ belongs to the $C^1$-interior of diffeomorphisms for which the $C^0$-transversality condition is not satisfied, $(ii)$ $f$ has a saddle connection. These results are based on the following theorem: if the phase diagram of an $\Omega$-stable diffeomorphism $f$ of a manifold $M$ of arbitrary dimension does not contain chains of length $m > 3$, then $f$ has the weak shadowing property.
    Mathematics Subject Classification: 37B99, 37C50, 37C75, 37D15, 37D20.


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

Article Metrics

HTML views() PDF downloads(118) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint