Entropy theory for sectional hyperbolic flows

IF 1.8 1区数学 Q1 MATHEMATICS, APPLIED

Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-07-01 DOI:10.1016/j.anihpc.2020.10.001

Maria José Pacifico , Fan Yang , Jiagang Yang

引用次数: 20

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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截面双曲流的熵理论

我们将熵理论作为一种新的工具来研究任意维度的截面双曲流。我们证明了对于C1流，每个截面双曲集Λ都是熵膨胀的，并且拓扑熵随流连续变化。更进一步，如果Λ是李雅普诺夫稳定的，则它具有正熵;另外，如果Λ是一个链循环类，那么它包含一个周期轨道。作为推论，我们证明了对于C1泛型流，每个类洛伦兹类都是吸引子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annales De L Institut Henri Poincare-Analyse Non Lineaire 数学-应用数学

CiteScore

4.10

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Nonlinear Analysis section of the Annales de l''Institut Henri Poincaré is an international journal created in 1983 which publishes original and high quality research articles. It concentrates on all domains concerned with nonlinear analysis, specially applicable to PDE, mechanics, physics, economy, without overlooking the numerical aspects.