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Entropy theory for sectional hyperbolic flows

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arxiv 1901.07436 v3 pith:OJLVMZ5J submitted 2019-01-22 math.DS

Maria Jose Pacifico , Fan Yang , Jiagang Yang This is my paper · ORCID
classification math.DS
keywords entropyflowshyperboliclambdasectionalclasseverythen
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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 $\Lambda$ is entropy expansive, and the topological entropy varies continuously with the flow. Furthermore, if $\Lambda$ is Lyapunov stable, then it has positive entropy; in addition, if $\Lambda$ 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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  1. A countable partition for singular flows, and its application on the entropy theory

    math.DS 2019-08 conditional novelty 7.0 of 10

    Hyperbolic singularities can be surrounded by a finite-entropy countable partition whose atoms control scaled tubular neighborhoods, yielding entropy formulas and upper semi-continuity away from tangencies.

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