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arXiv · 1310.8118

On the singular hyperbolicity of star flows

Yi Shi·Shaobo Gan·Lan Wen
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Abstract

We prove for a generic star vector field $X$ that, if for every chain recurrent class $C$ of $X$ all singularities in $C$ have the same index, then the chain recurrent set of $X$ is singular hyperbolic. We also prove that every Lyapunov stable chain recurrent class of $X$ is singular hyperbolic. As a corollary, we prove that the chain recurrent set of a generic 4-dimensional star flow is singular hyperbolic.

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Yi Shi, Shaobo Gan, Lan Wen. 2014-08-27. On the singular hyperbolicity of star flows. https://arxiv.org/abs/1310.8118

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