Two flows are almost commensurable if, up to removing finitely many periodic orbits and taking finite coverings, they are topologically equivalent. We prove that all suspensions of automorphisms of the 2-dimensional torus and all geodesic flows on unit tangent bundles to hyperbolic 2-orbifolds are pairwise almost commensurable.
Deux flots sont dits presque commensurables si, quitte à retirer à chacun un nombre fini dʼorbites périodiques puis prendre un revêtement fini, ils sont topologiquement équivalents. On montre que toutes les suspensions dʼautomorphismes hyperboliques du tore de dimension 2 et tous les flots géodésiques sur les fibrés unitaires tangents dʼorbisurfaces hyperboliques sont deux à deux presque commensurables.
Accepted:
Published online:
Pierre Dehornoy 1
@article{CRMATH_2013__351_3-4_127_0, author = {Pierre Dehornoy}, title = {Almost commensurability of 3-dimensional {Anosov} flows}, journal = {Comptes Rendus. Math\'ematique}, pages = {127--129}, publisher = {Elsevier}, volume = {351}, number = {3-4}, year = {2013}, doi = {10.1016/j.crma.2013.02.012}, language = {en}, }
Pierre Dehornoy. Almost commensurability of 3-dimensional Anosov flows. Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 127-129. doi : 10.1016/j.crma.2013.02.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.02.012/
[1] Geodesic flows on closed Riemannian manifolds with negative curvature, Proc. Steklov Inst. Math., Volume 90 (1967)
[2] Dynamical systems with two degrees of freedom, Trans. Amer. Math. Soc., Volume 18 (1917), pp. 199-300
[3] Genus one Birkhoff sections for geodesic flows (preprint) | arXiv
[4] Invariants of contact structures from open books, Trans. Amer. Math. Soc., Volume 260 (2008), pp. 3133-3151
[5] Transitive Anosov flows and pseudo-Anosov maps, Topology, Volume 22 (1983), pp. 299-303
[6] Flots dʼAnosov sur les 3-variétés fibrées en cercles, Ergodic Theory Dynam. Systems, Volume 4 (1984), pp. 67-80
[7] Sur lʼinvariance topologique de la classe de Godbillon–Vey, Ann. Inst. Fourier, Volume 37 (1987), pp. 59-76
[8] Les surfaces à courbures opposées et leurs lignes géodésiques, J. Math. Pures Appl., Volume 4 (1898), pp. 27-74
[9] On the Anosov diffeomorphisms corresponding to geodesic flow on negatively curved closed surfaces, J. Fac. Sci. Univ. Tokyo, Volume 37 (1990), pp. 485-494
[10] Self-mapping degrees of torus bundles and torus semi-bundles, Osaka J. Math., Volume 47 (2010), pp. 131-155
Cited by Sources:
Comments - Policy