| Abstract: |
| Let $X$ be a $C^1$ vector field of a closed smooth Riemannian manifold $M$ with dim$M \geq 3$ and $\gamma$ be a hyperbolic closed orbit of $X.$ In this talk, we introduce the notion of $C^1$ stably weak measure expansiveness of closed invariant set $\Lambda \subset M.$ And we show that the homoclinic class $H_X(\gamma)$ of $X$ associated to $\gamma$ is $C^1$ stably weak measure expansive if and only if it is hyperbolic. |
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