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.
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.
Accepted:
Published online:
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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