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Statistics of closest return for some non-uniformly hyperbolic systems

Published online by Cambridge University Press:  30 March 2001

P. COLLET
P. COLLET
Affiliation:
Centre de Physique Théorique, Laboratoire CNRS UMR 7644, Ecole Polytechnique, F-91128 Palaiseau Cedex, France (e-mail: collet@cpht.polytechnique.fr)
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Abstract

For non-uniformly hyperbolic maps of the interval with exponential decay of correlations we prove that the law of closest return to a given point when suitably normalized is almost surely asymptotically exponential. A similar result holds when the reference point is the initial point of the trajectory. We use the framework for non-uniformly hyperbolic dynamical systems developed by L. S. Young.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 2 , April 2001 , pp. 401 - 420
Copyright
2001 Cambridge University Press

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