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Kinematic N-expansive flows. (arXiv:1802.03104v1 [math.DS])
来源于:arXiv
In light of the rich results of expansiveness in the dynamics of
diffeomorphisms, it is natural to consider another notions of expansiveness
such as countably-expansive, measure expansive, $N$-expansive and so on. In
this paper, we introduce the notion of $N$-expansiveness for flows on a
$C^{\infty}$ compact connected Riemannian manifold by using the kinematic
expansiveness which is extension of the $N$-expansive diffeomorphisms. And we
prove that a vector field $X$ on $M$ is $C^1$ robustly kinematic $N$-expansive
then $X$ satisfies quasi-Anosov. Furthermore, we consider the hyperbolicity of
local dynamical systems with kinematic $N$-expansiveness. 查看全文>>