JournalsaihpcVol. 38, No. 4pp. 1001–1030

Entropy theory for sectional hyperbolic flows

  • Maria José Pacifico

    Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, RJ, Brazil

  • Fan Yang

    Department of Mathematics, University of Oklahoma, Norman, OK, USA

  • Jiagang Yang

    Department of Mathematics, Southern University of Science and Technology of China, Guangdong, China, Departamento de Geometria, Instituto de Matemática e Estatística, Universidade Federal Fluminense, Niterói, Brazil
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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 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 generic flows, every Lorenz-like class is an attractor.

Cite this article

Maria José Pacifico, Fan Yang, Jiagang Yang, Entropy theory for sectional hyperbolic flows. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 4, pp. 1001–1030

DOI 10.1016/J.ANIHPC.2020.10.001