Geodesic
$C^1$-Stably Positively Expansive Maps
Kazuhiro Sakai 1
1 Department of Mathematics Utsunomiya University Utsunomiya 321-8505, Japan
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 2, pp. 197-209 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba52-2-10
Keywords: notion stably positively expansive differentiable maps closed infty manifolds introduced proved differentiable map stably positively expansive only expanding furthermore maps varepsilon time dependent stability shown result every expanding map varepsilon time dependent stable

Kazuhiro Sakai  1

1 Department of Mathematics Utsunomiya University Utsunomiya 321-8505, Japan 
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Kazuhiro Sakai. $C^1$-Stably Positively Expansive Maps. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 2, pp. 197-209. doi: 10.4064/ba52-2-10

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