$C^1$-Stably Positively Expansive Maps

Volume 52 / 2004

Kazuhiro Sakai Bulletin Polish Acad. Sci. Math. 52 (2004), 197-209 MSC: Primary 37C50, 37C75, 37D20. DOI: 10.4064/ba52-2-10


The notion of $C^1$-stably positively expansive differentiable maps on closed $C^\infty $ manifolds is introduced, and it is proved that a differentiable map $f$ is $C^1$-stably positively expansive if and only if $f$ is expanding. Furthermore, for such maps, the $\varepsilon $-time dependent stability is shown. As a result, every expanding map is $\varepsilon $-time dependent stable.


  • Kazuhiro SakaiDepartment of Mathematics
    Utsunomiya University
    Utsunomiya 321-8505, Japan

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