The $ {C}^{0}$ general density theorem for geodesic flows

Mário Bessa; Maria Joana Torres

doi:10.1016/j.crma.2015.03.012

Dynamical systems

The

C^{0}

general density theorem for geodesic flows
[Le théorème de densité de Pugh

C^{0}

pour les flots géodésiques]

Présenté par : Jean-Christophe Yoccoz

Mário Bessa ¹ ; Maria Joana Torres ²

¹ CMA-UBI, Departamento de Matemática, Universidade da Beira Interior, Rua Marquês d'Ávila e Bolama, 6201-001 Covilhã, Portugal
² CMAT, Departamento de Matemática e Aplicações, Universidade do Minho, Campus de Gualtar, 4700-057 Braga, Portugal

Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 545-549.

Abstract (VO)
Résumé

Given a closed Riemannian manifold, we prove the $C^{0}$ -general density theorem for continuous geodesic flows. More precisely, we prove that there exists a residual (in the $C^{0}$ -sense) subset of the continuous geodesic flows such that, in that residual subset, the geodesic flow exhibits dense closed orbits.

Étant donnée une variété riemannienne compacte sans bord, nous démontrons un théorème de densité $C^{0}$ -générique pour les flots géodésiques et, plus précisément, nous prouvons qu'il existe une partie $C^{0}$ -résiduelle de l'ensemble des flots géodésiques continus, telle que tout flot dans cette partie admet un ensemble dense d'orbites périodiques.

Reçu le : 2014-05-21
Accepté le : 2015-03-02
Publié le : 2015-04-04

DOI : 10.1016/j.crma.2015.03.012

Affiliations des auteurs :

Mário Bessa ¹ ; Maria Joana Torres ²

¹ CMA-UBI, Departamento de Matemática, Universidade da Beira Interior, Rua Marquês d'Ávila e Bolama, 6201-001 Covilhã, Portugal
² CMAT, Departamento de Matemática e Aplicações, Universidade do Minho, Campus de Gualtar, 4700-057 Braga, Portugal

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Mário Bessa; Maria Joana Torres. The $ {C}^{0}$ general density theorem for geodesic flows. Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 545-549. doi : 10.1016/j.crma.2015.03.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.03.012/

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Assis Azevedo; Davide Azevedo; Mário Bessa; Maria Joana Torres The closing lemma and the planar general density theorem for Sobolev maps, Proceedings of the American Mathematical Society, Volume 149 (2021) no. 4, pp. 1687-1696 | DOI:10.1090/proc/15352 | Zbl:1470.37069
Mário Bessa A note on expansiveness and hyperbolicity for generic geodesic flows, Mathematical Physics, Analysis and Geometry, Volume 21 (2018) no. 2, p. 9 (Id/No 14) | DOI:10.1007/s11040-018-9271-7 | Zbl:1395.37018
Mário Bessa; Maria Joana Torres; Paulo Varandas On the periodic orbits, shadowing and strong transitivity of continuous flows, Nonlinear Analysis. Theory, Methods Applications. Series A: Theory and Methods, Volume 175 (2018), pp. 191-209 | DOI:10.1016/j.na.2018.06.002 | Zbl:1404.53111

Cité par 3 documents. Sources : zbMATH

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