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Law of the iterated logarithm for transitiveC 2 Anosov flows and semiflows over maps of the interval

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Abstract

It is proved that a functional law of the iterated logarithm is valid for transitiveC 2 Anosov flows on compact Riemannian manifolds when the observable belongs to a certain class of real-valued Hölder functions. The result is equally valid for semiflows over piecewise expanding interval maps that are similar to the Williams' Lorenz-attractor semiflows. Furthermore the observables need only be real-valued Hölder for these semiflows.

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References

  1. Billingsley, P.: Convergence of Probability Measures. New York: Wiley. 1968.

    Google Scholar 

  2. Bowen, R.: Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. Lecture Notes Math. 470. Berlin-Heidelberg-New York: Springer. 1975.

    Google Scholar 

  3. Bowen, R., Ruelle, D.: The ergodic theory of Axiom-A flows. Invent. Math.18, 181–202 (1975).

    Google Scholar 

  4. Hofbauer, F., Keller, G.: Ergodic properties of invariant measures for piecewise monotonic transformations. Preprint. Universität Göttingen. 1981.

  5. Ibragimov, I. A.: Some limit theorems for stationary processes. Th. Prob. Appl.7, 349–382 (1962).

    Google Scholar 

  6. Leonov, V. P.: On the dispersion of time-dependent means of a stationary stochastic process. Th. Prob. Appl.6, 87–93 (1961).

    Google Scholar 

  7. Ratner, M.: The central limit theorem for geodesic flows onn-dimensional manifolds of negative curvature. Israel J. Math.16, 181–197 (1973).

    Google Scholar 

  8. Ratner, M.: Bernoulli flows over maps of the interval. Israel J. Math.31, 298–314 (1978).

    Google Scholar 

  9. Reznik, M. Kh.: The law of the iterated logarithm for some classes of stationary processes. Th. Prob. Appl.13, 606–621 (1968).

    Google Scholar 

  10. Williams, R. F.: The structure of Lorenz attractors. IHES Publ. Math.50, 321–347 (1979).

    Google Scholar 

  11. Wong, S.: Two probabilistic properties of weak-Bernoulli interval maps. (To appear.)

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  1. Baruch College, The City University of New York, 17 Lexington Avenue, 10010, New York, NY, USA

    Sherman Wong

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  1. Sherman Wong
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Wong, S. Law of the iterated logarithm for transitiveC 2 Anosov flows and semiflows over maps of the interval. Monatshefte für Mathematik 94, 163–173 (1982). https://doi.org/10.1007/BF01301935

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  • DOI: https://doi.org/10.1007/BF01301935

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