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arXiv · 2101.09480

An entropy dichotomy for singular star flows

Maria José Pacifico·Fan Yang·Jiagang Yang
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Abstract

We show that non-trivial chain recurrent classes for generic $C^1$ star flows satisfy a dichotomy: either they have zero topological entropy, or they must be isolated. Moreover, chain recurrent classes for generic star flows with zero entropy must be sectional hyperbolic, and cannot be detected by any non-trivial ergodic invariant probability. As a result, we show that $C^1$ generic star flows have only finitely many Lyapunov stable chain recurrent classes.

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Maria José Pacifico, Fan Yang, Jiagang Yang. 2021-01-23. An entropy dichotomy for singular star flows. https://arxiv.org/abs/2101.09480

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