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    AARONSON, JON and DENKER, MANFRED 2001. LOCAL LIMIT THEOREMS FOR PARTIAL SUMS OF STATIONARY SEQUENCES GENERATED BY GIBBS–MARKOV MAPS. Stochastics and Dynamics, Vol. 01, Issue. 02, p. 193.


    Coelho, Zaqueu 1993. On the asymptotic range of cocyles for shifts of finite type. Ergodic Theory and Dynamical Systems, Vol. 13, Issue. 02,


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  • Ergodic Theory and Dynamical Systems, Volume 9, Issue 3
  • September 1989, pp. 433-453

Propriétés ergodiques, en mesure infinie, de certains systèmes dynamiques fibrés

  • Y. Guivarc'h (a1)
  • DOI: http://dx.doi.org/10.1017/S0143385700005083
  • Published online: 01 September 2008
Abstract
Abstract

We study the ergodic properties of a class of dynamical systems with infinite invariant measure. This class contains skew-products of Anosov systems with ℝd. The results are applied to the K property of skew-products and also to the ergodicity of the geodesic flow on abelian coverings of compact manifolds with constant negative curvature.

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[1]R.L. Adler & P. C. Shields . Skew products of Bernoulli shifts with rotations. Israël J. Math. 19 (1974), 228236.

[3]R. Bowen . Symbolic dynamics for hyperbolic flows. Amer. J. Math. 95 (1973), 429460.

[4]R. Bowen & D. Ruelle . The ergodic theory of axiom A flows. Inventiones Math. 29 (1975), 181202.

[5]L.A. Bunimovich & Ya G. Sinai . Statistical properties of Lorentz gas with periodic configurations. Commun. Math. Phys. 78 (1981), 479497.

[10]Y. Guivarc'h , M. Keane & B. Roynette . Marches aleatoires sur les groupes de Lie. Lecture Notes in Mathematics 624 (Springer-Verlag, Berlin, 1977).

[12]S. Kalikow . T, T−1 transformation is not loosely Bernoulli. Ann. Math. 115 (1982), 393409.

[13]A. Katok . Smooth non-Bernoulli K -automorphisms. Inventiones Math. 61 (1980), 291300.

[16]M. Lin . Mixing for Markov operators. Z. Wahr. 19 (1971), 231242.

[21]S. Smale . Differentiate dynamical systems. Bull. Amer. Math. Soc. 73 (1967), 747817.

[22]Ya G. Sinai . Gibbs measures in ergodic theory. Russian Math. Surveys 27 (4) (1972), 2169.

[23]F. Spitzer . Principles of random walks. Van Nostrand, Princeton, 1964.

[24]D. Sullivan . The density at infinity of a discrete groupe of hyperbolic motions. I.H.E.S. Publ. Math. 50 (1979), 171202.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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