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Entropy theory for sectional hyperbolic flows
Annales de l'Institut Henri Poincaré C, Analyse non linéaire ( IF 1.9 ) Pub Date : 2020-10-14 , DOI: 10.1016/j.anihpc.2020.10.001
Maria José Pacifico 1 , Fan Yang 2 , Jiagang Yang 3, 4
Affiliation  

We use entropy theory as a new tool to study sectional hyperbolic flows in any dimension. We show that for C1 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 C1 generic flows, every Lorenz-like class is an attractor.



中文翻译:

截面双曲流的熵理论

我们使用熵理论作为研究任何维度的截面双曲流的新工具。我们证明对于C1流,每个截面双曲集 Λ 是熵膨胀的,拓扑熵随流连续变化。此外,如果 Λ 是李雅普诺夫稳定的,则它具有正熵;此外,如果Λ是链循环类,则它包含一个周期轨道。作为推论,我们证明对于C1 泛型流,每个 Lorenz-like 类都是一个吸引子。

更新日期:2020-10-14
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