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arXiv · 0903.4090

Generic bi-Lyapunov stable homoclinic classes

Rafael Potrie
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Abstract

We study, for $C^1$ generic diffeomorphisms, homoclinic classes which are Lyapunov stable both for backward and forward iterations. We prove they must admit a dominated splitting and show that under some hypothesis they must be the whole manifold. As a consequence of our results we also prove that in dimension 2 the class must be the whole manifold and in dimension 3, these classes must have nonempty interior. Many results on Lyapunov stable homoclinic classes for $C^1$-generic diffeomorphisms are also deduced.

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Rafael Potrie. 2010-05-12. Generic bi-Lyapunov stable homoclinic classes. https://doi.org/10.1088/0951-7715%2F23%2F7%2F006

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