Strong symbolic dynamics for geodesic flow on CAT(-1) spaces and other metric Anosov flows
| Autor: | Constantine, David, Lafont, Jean-François, Thompson, Daniel J. |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | J. \'Ec. Polytech. Math. 7 (2020), pgs. 201-231 |
| Druh dokumentu: | Working Paper |
| Popis: | We prove that the geodesic flow on a locally CAT(-1) metric space which is compact, or more generally convex cocompact with non-elementary fundamental group, can be coded by a suspension flow over an irreducible shift of finite type with H\"older roof function. This is achieved by showing that the geodesic flow is a metric Anosov flow, and obtaining H\"older regularity of return times for a special class of geometrically constructed local cross-sections to the flow. We obtain a number of strong results on the dynamics of the flow with respect to equilibrium measures for H\"older potentials. In particular, we prove that the Bowen-Margulis measure is Bernoulli except for the exceptional case that all closed orbit periods are integer multiples of a common constant. We show that our techniques also extend to the geodesic flow associated to a projective Anosov representation, which verifies that the full power of symbolic dynamics is available in that setting. Comment: v4: 28 pages, 4 figures. Final version, to appear in Journal de l'Ecole polytechnique |
| Databáze: | arXiv |
| Externí odkaz: |
|