Israel Journal of Mathematics

, Volume 130, Issue 1, pp 29–75 | Cite as

Backward inducing and exponential decay of correlations for partially hyperbolic attractors

  • Augusto Armando
  • Castro Júnior


We study partially hyperbolic attractors ofC 2 diffeomorphisms on a compact manifold. For a robust (non-empty interior) class of such diffeomorphisms, we construct Sinai-Ruelle-Bowen measures, for which we prove exponential decay of correlations and the central limit theorem, in the space of Hölder continuous functions. The techniques we develop (backward inducing, redundancy elimination algorithm) should be useful in the study of the stochastic properties of much more general non-uniformly hyperbolic systems.


Exponential Decay Central Limit Theorem Markov Partition Stable Leaf Hyperbolic Attractor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. F. Alves,SRB measures for nonhyperbolic systems with multidimensional expansion, PhD thesis, IMPA, 1997.Google Scholar
  2. [2]
    C. Bonatti and M. Viana,SRB measures for partially hyperbolic systems whose central direction is mostly contracting, Israel Journal of Mathematics115 (2000), 157–193.MATHMathSciNetGoogle Scholar
  3. [3]
    M. Brin and Ya. Pesin,Partially hyperbolic dynamical systems, Izvestiya Akademii Nauk SSSR1 (1974), 177–212.CrossRefGoogle Scholar
  4. [4]
    M. Carvalho,Sinai-Ruelle-Bowen measures for N-dimensional derived from Anosov diffeomorphisms, Ergodic Theory and Dynamical Systems13 (1993), 21–44.MATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    A. A. Castro,Backward inducing and exponential decay of correlations for partially hyperbolic attractors with mostly contracting central direction, PhD thesis, IMPA, 1998.Google Scholar
  6. [6]
    D. Dolgopyat,On dynamics of mostly contracting diffeomorphisms, Preprint, 1998.Google Scholar
  7. [7]
    M. Hirsch, C. Pugh and M. Shub,Invariant manifold, Lecture Notes in Mathematics583, Springer-Verlag, Berlin, 1977.Google Scholar
  8. [8]
    C. Livernani,Decay of correlations, Annals of Mathematics142 (1995), 239–301.CrossRefMathSciNetGoogle Scholar
  9. [9]
    R. Mañe,Ergodic Theory and Differentiable Dynamics, Springer-Verlag, Berlin, 1987.MATHGoogle Scholar
  10. [10]
    Ya. Pesin and Ya. Sinai,Gibbs measures for partially hyperbolic attractors, Ergodic Theory and Dynamical Systems2 (1982), 417–438.MATHMathSciNetGoogle Scholar
  11. [11]
    C. Pugh and M. Shub,Ergodic attractors, Transactions of the American Mathematical Society312 (1989), 1–54.MATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    M. Shub,Global Stability of Dynamica Systems, Springer-Verlag, Berlin, 1987.Google Scholar
  13. [13]
    M. Viana,Stochastic dynamics of deterministic systems, Lecture Notes from the XXI Brazilian Mathematical Colloqium, IMPA, Rio de Janeiro, 1997.Google Scholar
  14. [14]
    L.-S. Young,Statistical properties of dynamicals systems with some hyperbolicity, Annals of Mathematics147 (1998), 585–650.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University 2002

Authors and Affiliations

  1. 1.Federal University of Ceará (UFC)FortalezaBrazil

Personalised recommendations