Geodesic
Entropy theory for sectional hyperbolic flows
José Pacifico, Maria1 ; Yang, Fan2 ; Yang, Jiagang3, 4
1 a Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, RJ, Brazil
2 b Department of Mathematics, University of Oklahoma, Norman, OK, USA
3 c Department of Mathematics, Southern University of Science and Technology of China, Guangdong, China
4 d Departamento de Geometria, Instituto de Matemática e Estatística, Universidade Federal Fluminense, Niterói, Brazil
Annales de l'I.H.P. Analyse non linéaire, juillet – août 2021, Tome 38 (2021) no. 4, pp. 1001-1030

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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.

Reçu le :
Révisé le :
Accepté le :
DOI : 10.1016/j.anihpc.2020.10.001
Keywords: Entropy, Entropy expansive, Lorenz like attractors, Sectional hyperbolic flows

José Pacifico, Maria 1 ; Yang, Fan 2 ; Yang, Jiagang 3, 4

1 a Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, RJ, Brazil
2 b Department of Mathematics, University of Oklahoma, Norman, OK, USA
3 c Department of Mathematics, Southern University of Science and Technology of China, Guangdong, China
4 d Departamento de Geometria, Instituto de Matemática e Estatística, Universidade Federal Fluminense, Niterói, Brazil 
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     title = {Entropy theory for sectional hyperbolic flows},
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     pages = {1001--1030},
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José Pacifico, Maria; Yang, Fan; Yang, Jiagang. Entropy theory for sectional hyperbolic flows. Annales de l'I.H.P. Analyse non linéaire, juillet – août 2021, Tome 38 (2021) no. 4, pp. 1001-1030. doi: 10.1016/j.anihpc.2020.10.001

Cité par Sources :

M.J.P. and J.Y. are partially supported by Grant Produtividade em Pesquisa ( CNPq ), Grant Cientista do Nosso Estado ( FAPERJ ), PROEX-CAPES . F.Y. would like to thank the hospitality of Southern University of Science and Technology of China (SUSTC), where part of this work is done.