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Equations for the entropy of a geodesic flow on a compact Riemannian manifold without conjugate points

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Literature cited

  1. D. Gromoll, W. Klingenberg, and W. Meyer, Riemannian Geometry in the Large [Russian translation], Mir, Moscow (1971).

    Google Scholar 

  2. S. Lang, Introduction to Differentiable Manifolds, Wiley-Interscience, New York (1962).

    Google Scholar 

  3. V. A. Rokhlin, “Lectures on the entropie theory of transformations with invariant measure,” Usp. Mat. Nauk,22, No. 5, 4–51 (1967).

    Google Scholar 

  4. V. I. Oseledets, “Multiplicative ergodic theorem. Lyapunov characteristic exponents of dynamical systems,” Tr. Mosk. Mat. Obshchestva,19, 179–210 (1968).

    Google Scholar 

  5. Ya. B. Pesin, “Lyapunov characteristic exponents and smooth ergodic theory,” Usp. Mat. Nauk,32, No. 4, 55–111 (1977).

    Google Scholar 

  6. P. Eberlein, “When is a geodesic flow of Anosov type. I,” J. Differential Geometry,8, No. 3, 437–463 (1973).

    Google Scholar 

  7. Ya. B. Pesin, “Geodesic flows on closed Riemannian manifolds without focal points,” Izv. Akad. Nauk SSSR, Ser. Mat.,41, No. 6, 1252–1288 (1977).

    Google Scholar 

  8. P. Eberlein, “Geodesic flow in certain manifolds without conjugate points,” Trans. Am. Math. Soc.,167, 151–270 (1972).

    Google Scholar 

  9. W. Klingenberg, “Riemannian manifolds with geodesic flow of Anosov type,” Ann. Math.,99, 1–13 (1974).

    Google Scholar 

  10. P. Eberlein, “Geodesic flows on negatively curved manifolds. I,” Ann. Math.,95, 492–510 (1972).

    Google Scholar 

  11. E. Heinfze and H.-C. Im Hof, “On the geometry of horospheres,” Preprint, Bonn (1975).

  12. J. H. Eschenburg, “Horospheres and the stable part of the geodesic flow,” Math. Z.,1953, 237–251 (1977).

    Google Scholar 

  13. L. W. Green, “A theorem of E. Hopf,” Michigan Math. J.,5, 31–34 (1958).

    Google Scholar 

  14. V. I. Arnold, Ordinary Differential Equations, MIT Press (1973).

  15. Ya. B. Pesin, “Families of invariant manifolds, corresponding to nonzero characteristic exponents,” Izv. Akad. Nauk SSSR, Ser. Mat.,40, No. 6, 1332–1379 (1976).

    Google Scholar 

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Authors and Affiliations

  1. All-Union Scientific-Research Institute for Opticophysical Measurements, USSR

    Ya. B. Pesin

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  1. Ya. B. Pesin
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Translated from Matematicheskie Zametki, Vol. 24, No. 4, pp. 553–570, October, 1978.

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Pesin, Y.B. Equations for the entropy of a geodesic flow on a compact Riemannian manifold without conjugate points. Mathematical Notes of the Academy of Sciences of the USSR 24, 796–805 (1978). https://doi.org/10.1007/BF01099169

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  • DOI: https://doi.org/10.1007/BF01099169

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