References
[B-G] Brin, M. Gromov, M.: On the ergodicity of frame flows. Invent. Math.60, 1–7 (1980)
[C] Chavel, I.: Riemannian symmetric spaces of rank one. Lecture Notes in Pure and Applied Mathematics, vol. 5. New York: Marcel Dekker 1972
[E] Eberlein, P.: When is a geodesic flow of Anosov type? J. Diff. Geom.8, 437–463 (1973)
[F-M] Freire, A., Mañé, R.: On the entropy of the geodesic flow in manifolds without conjugate points. Invent. Math.69, 375–392 (1982)
[G] Green, L.W.: A theorem of E. Hopf. Michigan Math. J.5, 31–34 (1958)
[H] Heintze, E.: On homogeneous manifolds of negative curvature. Math. Ann.211, 23–34 (1974)
[K] Katok, A.: Entropy and closed geodesics. Ergodic Th. and Dynam. Sys.2, 339–367 (1982)
[M] Manning, A.: Curvature bounds for the entropy of the geodesie flow on a surface. J. Lond. Math. Soc. (2)24, 351–357 (1981)
[P] Pesin, Ya.B.: Characteristic Lyapunov exponents and smooth ergodic theory Russ. Math. Surveys (4)32, 55–114 (1977)
[SA1] Sarnak, P.: Prime geodesic theorems. Ph. D. Thesis, Stanford 1980
[SA2] Sarnak, P.: Entropy estimates for geodesic flows. Ergod. Th. and Dynam. Systems2, 513–524 (1982)
[S] Sinai, Ya.G.: The asymptotic behavior of the number of clsed geodesics on a compact manifold of negative curvature. Izv. Akad. Nauk SSSR, Ser. Math.30, 1275–1295 (1966); English translation, A.M.S. Trans.73,(2) 229–250 (1968)
[SP] Spatzier, R.: Dynamical properties of algebraic systems; a study in closed geodesics. Ph.D. Thesis, Warwick 1983
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Osserman, R., Sarnak, P. A new curvature invariant and entropy of geodesic flows. Invent Math 77, 455–462 (1984). https://doi.org/10.1007/BF01388833
Issue Date:
DOI: https://doi.org/10.1007/BF01388833