Geodesic
Dynamical systems
The C0 general density theorem for geodesic flows
[Le théorème de densité de Pugh C0 pour les flots géodésiques]

Présenté par : Jean-Christophe Yoccoz

Bessa, Mário1 ; Torres, Maria Joana2
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, Tome 353 (2015) no. 6, pp. 545-549.

Voir la notice de l'article provenant de la source Numdam

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.

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

Bessa, Mário 1 ; Torres, Maria Joana 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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Bessa, Mário; Torres, Maria Joana. The $ {C}^{0}$ general density theorem for geodesic flows. Comptes Rendus. Mathématique, Tome 353 (2015) no. 6, pp. 545-549. doi : 10.1016/j.crma.2015.03.012. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2015.03.012/

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