Backward inducing and exponential decay of correlations for partially hyperbolic attractors
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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.
KeywordsExponential Decay Central Limit Theorem Markov Partition Stable Leaf Hyperbolic Attractor
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- J. F. Alves,SRB measures for nonhyperbolic systems with multidimensional expansion, PhD thesis, IMPA, 1997.Google Scholar
- 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
- D. Dolgopyat,On dynamics of mostly contracting diffeomorphisms, Preprint, 1998.Google Scholar
- M. Hirsch, C. Pugh and M. Shub,Invariant manifold, Lecture Notes in Mathematics583, Springer-Verlag, Berlin, 1977.Google Scholar
- M. Shub,Global Stability of Dynamica Systems, Springer-Verlag, Berlin, 1987.Google Scholar
- M. Viana,Stochastic dynamics of deterministic systems, Lecture Notes from the XXI Brazilian Mathematical Colloqium, IMPA, Rio de Janeiro, 1997.Google Scholar