[Le théorème de densité de Pugh pour les flots géodésiques]
Étant donnée une variété riemannienne compacte sans bord, nous démontrons un théorème de densité -générique pour les flots géodésiques et, plus précisément, nous prouvons qu'il existe une partie -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 -general density theorem for continuous geodesic flows. More precisely, we prove that there exists a residual (in the -sense) subset of the continuous geodesic flows such that, in that residual subset, the geodesic flow exhibits dense closed orbits.
Accepté le :
Publié le :
Mário Bessa 1 ; Maria Joana Torres 2
@article{CRMATH_2015__353_6_545_0,
author = {M\'ario Bessa and Maria Joana Torres},
title = {The $ {C}^{0}$ general density theorem for geodesic flows},
journal = {Comptes Rendus. Math\'ematique},
pages = {545--549},
publisher = {Elsevier},
volume = {353},
number = {6},
year = {2015},
doi = {10.1016/j.crma.2015.03.012},
language = {en},
}
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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