Comptes Rendus
Dynamical systems
The C0 general density theorem for geodesic flows
[Le théorème de densité de Pugh C0 pour les flots géodésiques]
Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 545-549.

Étant donnée une variété riemannienne compacte sans bord, nous démontrons un théorème de densité C0-générique pour les flots géodésiques et, plus précisément, nous prouvons qu'il existe une partie C0-résiduelle de l'ensemble des flots géodésiques continus, telle que tout flot dans cette partie admet un ensemble dense d'orbites périodiques.

Given a closed Riemannian manifold, we prove the C0-general density theorem for continuous geodesic flows. More precisely, we prove that there exists a residual (in the C0-sense) subset of the continuous geodesic flows such that, in that residual subset, the geodesic flow exhibits dense closed orbits.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.03.012

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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