$C^1$-Stably Positively Expansive Maps
Volume 52 / 2004
Bulletin Polish Acad. Sci. Math. 52 (2004), 197-209
MSC: Primary 37C50, 37C75, 37D20.
DOI: 10.4064/ba52-2-10
Abstract
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.
