Freire, A.; Mañé, R. On the entropy of the geodesic flow in manifolds without conjugate points. (English) Zbl 0476.58019 Invent. Math. 69, 375-392 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 ReviewsCited in 39 Documents MSC: 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 53D25 Geodesic flows in symplectic geometry and contact geometry 53C22 Geodesics in global differential geometry 54C70 Entropy in general topology 37A99 Ergodic theory 28D20 Entropy and other invariants Keywords:entropy of the geodesic flow in manifolds without conjugate points; boundaryless Riemannian manifold; volume growth rate; metric entropy; average of the Ricci tensor in the unit tangent bundle Citations:Zbl 0426.58016; Zbl 0421.58014 × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] Avez, A.: Variétés riemanniennes sans points focaux. C.R. Acad. Sci. Paris, Ser A-B270, A188-A191 (1970) · Zbl 0188.26402 [2] Dinaburg, E.I.: On the relations among various entropy characteristics of dynamical systems. Math. USSR Izv.5, 337-388 (1971) · Zbl 0248.58007 · doi:10.1070/IM1971v005n02ABEH001050 [3] Eberlein, P.: When is a geodesic flow of Anosov type? I. J. Differential Geometry8, 437-463 (1973) · Zbl 0285.58008 [4] Green, L.A.: A theorem of E. Hopf. Michigan Math. J.5, 31-34 (1958) · Zbl 0134.39601 · doi:10.1307/mmj/1028998009 [5] Katok, A.: Entropy and closed geodesics. Ergodic Theory and Dynamical Systems in press (1982) · Zbl 0525.58027 [6] Klingeberg, W.: Riemannian manifolds with geodesic flows of Anosov type. Ann. Math.99, 1-13 (1974) · Zbl 0272.53025 · doi:10.2307/1971011 [7] Manning, A.: Topological entropy for geodesic flows. Ann. Math.110, 567-573 (1979) · Zbl 0426.58016 · doi:10.2307/1971239 [8] Manning, A.: Curvature bounds for the entropy of the geodesic flow on a surface. J. of the London Math. Soc.24, 351-358 (1981) · Zbl 0443.53035 · doi:10.1112/jlms/s2-24.2.351 [9] Margulis, G.A.: Applications of ergodic theory to the investigation of manifolds of negative curvature. Funct. Anal. Appl.3, 335-336 (1969) · Zbl 0207.20305 [10] Milnor, J.: A note on curvature and fundamental group. J. Differential Geometry2, 1-17 (1968) · Zbl 0162.25401 [11] Oseledec, V.I.: A multiplicative ergodic theorem. Tras. Moscow Math. Soc.19, 197-231 (1968) [12] Pesin, Ya.: Lyapounov characteristic exponents and smooth ergotid theory. Usp. Math. Nauk32-4, 55-111 (1977) [13] Pesin, Ya.: Equations for the entropy of a geodesic flow on a compact Riemannian manifold without conjugate points. Notes in Mathematics24, 796-805 (1978) · Zbl 0411.58016 [14] Przytycki, F.: An Upper Estimation for Topological Entropy of Diffeomorphisms. Inventiones math.59, 205-213 (1980) · doi:10.1007/BF01453234 [15] Ruelle, D.: An inequality for the entropy of differentiable maps. Bol. Soc. Bras. Mat.9, 83-87 (1978) · Zbl 0432.58013 · doi:10.1007/BF02584795 [16] Sacksteder, R., Shub, M.: Entropy of a differentiable map. Advances in Mathematics28, 181-185 (1978) · Zbl 0414.58027 · doi:10.1016/0001-8708(78)90113-5 [17] Sarnak, P.: Entropy estimates for geodesic flows, Thesis, Stanford University · Zbl 0525.58028 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.