Decay of Correlations, Quantitative Recurrence and Logarithm Law for Contracting Lorenz Attractors

Decay of Correlations, Quantitative Recurrence and Logarithm Law for Contracting Lorenz Attractors In this paper we prove that a class of skew products maps with non uniformly hyperbolic base has exponential decay of correlations. We apply this to obtain a logarithm law for the hitting time associated to a contracting Lorenz attractor at all the points having a well defined local dimension, and a quantitative recurrence estimation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Statistical Physics Springer Journals

Decay of Correlations, Quantitative Recurrence and Logarithm Law for Contracting Lorenz Attractors

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Physics; Statistical Physics and Dynamical Systems; Theoretical, Mathematical and Computational Physics; Physical Chemistry; Quantum Physics
ISSN
0022-4715
eISSN
1572-9613
D.O.I.
10.1007/s10955-018-1972-6
Publisher site
See Article on Publisher Site

Abstract

In this paper we prove that a class of skew products maps with non uniformly hyperbolic base has exponential decay of correlations. We apply this to obtain a logarithm law for the hitting time associated to a contracting Lorenz attractor at all the points having a well defined local dimension, and a quantitative recurrence estimation.

Journal

Journal of Statistical PhysicsSpringer Journals

Published: Feb 3, 2018

References

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