Geodesic
Entropy theory for sectional hyperbolic flows
José Pacifico, Maria1 ; Yang, Fan2 ; Yang, Jiagang3, 4
1a Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, RJ, Brazil
2b Department of Mathematics, University of Oklahoma, Norman, OK, USA
3c Department of Mathematics, Southern University of Science and Technology of China, Guangdong, China
4d 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 :
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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.