Abstract
Abstract
In this paper we show that a geodesic flow of a compact surface without conjugate points of genus greater than one is time-preserving semi-conjugate to a continuous expansive flow which is topologically mixing and has a local product structure. As an application we show that the geodesic flow of a compact surface without conjugate points of genus greater than one has a unique measure of maximal entropy. This gives an alternative proof of Climenhaga–Knieper–War Theorem.
Funder
Instituto Nacional de Ciência e Tecnologia de Matemática
Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Reference30 articles.
1. Geodesic flows on closed Riemannian manifolds with negative curvature;Anosov;Trudy Mat. Inst. Steklov,1967
2. Entropy for group endomorphisms and homogeneous spaces;Bowen;Trans. Am. Math. Soc.,1971
3. Periodic orbits for hyperbolic flows;Bowen;Am. J. Math.,1972
4. Expansive one-parameter flows;Bowen;J. Differ. Equ.,1972
5. Maximal entropy measures for certain partially hyperbolic, derived from Anosov systems;Buzzi;Ergod. Theory Dyn. Syst.,2012