| Abstract: |
| Let $M$ be a closed $n$-dimensional smooth Riemmanian manifold,
and let $X$ be a $C^1$-vector field of $M.$ Let $\gamma$ be a
hyperbolic closed orbit of $X_t.$ In this talk, we show that (i)
the chain recurrent set $\mathcal{R}(X_t)$ is $C^1$-stably
expansive for flows if and only if $X_t$ satisfies both Axiom A
and the no-cycle condition. (ii) the homoclinic class
$H_X(\gamma)$ is $C^1$-stably expansive for flows if and only if
$H_X(\gamma)$ is hyperbolic. |
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