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Deviations of trajectory averages and the defect in Pesin's formula for Anosov diffeomorphisms


Authors: Steven Orey and Stephan Pelikan
Journal: Trans. Amer. Math. Soc. 315 (1989), 741-753
MSC: Primary 60F10; Secondary 28D20, 58F11, 58F15
DOI: https://doi.org/10.1090/S0002-9947-1989-0935534-4
MathSciNet review: 935534
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Abstract: A large deviation theorem at the Donsker Varadhan level three is obtained for the convergence of trajectory averages of Anosov diffeomorphisms. It is possible to provide an explicit description of the rate function.


References [Enhancements On Off] (What's this?)

  • [A] D. V. Anosov, Geodesic flows on closed Riemannian manifolds with negative curvature, Proc. Steklov Inst. Math., vol. 90, Amer. Math. Soc., Providence, R. I., 1969. MR 0242194 (39:3527)
  • [B] R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Math., vol. 470, Springer-Verlag, New York, 1975. MR 0442989 (56:1364)
  • [DV] M. Donsker and S. S. R. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, part 4, Comm. Pure Appl. Math. (1983), 183-212.
  • [L] F. Ledrappier, Propriétés ergodiques des mesures de Sinai, Inst. Hautes Études Sci. Publ. Math. (to appear). MR 743818 (86f:58092)
  • [ME] N. F. G. Martin and J. W. England, Mathematical theory of entropy, Addison-Wesley, Reading, Mass., 1981. MR 612318 (83k:28019)
  • [O] S. Orey, Large deviations in ergodic theory, Seminar on Stochastic Processes, Evanston, 1984 (E. Cinlar et al., eds.), Birkhäuser, Boston, Mass., 1986, pp. 195-259. MR 896730 (88j:60059)
  • [OP] S. Orey and S. Pelikan, Large deviation principles for stationary shifts, IMA preprint no. 227.
  • [P] J. B. Pesin, Characteristic Lyapunov exponents and smooth ergodic theory, Russian Math. Surveys 32 (1977), 55-114. MR 0466791 (57:6667)
  • [Ra] M. Ratner, Markov partitions for Anosov flows on $ n$-dimensional manifolds, Israel J. Math. 15 (1973), 92-114. MR 0339282 (49:4042)
  • [R] D. Ruelle, Thermodynamic formulations, Addison-Wesley, London, 1978. MR 511655 (80g:82017)
  • [S1] Ya. G. Sinai, Markov partitions and $ C$-diffeomorphisms, Functional Anal. Appl. 2 (1968), 70-80. MR 0250352 (40:3591)
  • [S2] -, Construction of Markov partitions, Functional Anal. Appl. 2 (1968), 245-253. MR 0250352 (40:3591)
  • [T] Y. Takahashi, Entropy functional (free energy) for dynamical systems and their random perturbations. Proc. Taniguchi Sympos. on Stochastic Analysis (Katata and Kyoto, eds.), Kinokuniga/ North-Holland, 1980. MR 780769 (86m:58089)
  • [V] S. S. R. Varadhan, Large deviations and applications, SIAM CBMS-NSF Regional Conference in Applied Math, no. 46, SIAM, Philadelphia, Pa., 1984. MR 758258 (86h:60067b)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1989-0935534-4
Keywords: Anosov diffeomorphism, trajectory average, large deviations
Article copyright: © Copyright 1989 American Mathematical Society

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