Comptes Rendus
Dynamical systems
The C0 general density theorem for geodesic flows
Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 545-549.

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.

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.

Received:
Accepted:
Published online:
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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