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arXiv · 1901.07436

Entropy theory for sectional hyperbolic flows

Maria Jose Pacifico·Fan Yang·Jiagang Yang
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Abstract

We use entropy theory as a new tool to study sectional hyperbolic flows in any dimension. We show that for $C^1$ flows, every sectional hyperbolic set $Λ$ is entropy expansive, and the topological entropy varies continuously with the flow. Furthermore, if $Λ$ is Lyapunov stable, then it has positive entropy; in addition, if $Λ$ is a chain recurrent class, then it contains a periodic orbit. As a corollary, we prove that for $C^1$ generic flows, every Lorenz-like class is an attractor.

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Maria Jose Pacifico, Fan Yang, Jiagang Yang. 2020-07-15. Entropy theory for sectional hyperbolic flows. https://arxiv.org/abs/1901.07436

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