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Poisson law for Axiom A diffeomorphisms

Published online by Cambridge University Press:  19 September 2008

Masaki Hirata
Masaki Hirata
Affiliation:
Department of Pure and Applied Sciences, University of Tokyo, Komaba, Meguro-ku, Tokyo 153, Japan
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Abstract

Let f be an Axiom A diffeomorphism, Ω its non wandering set, µ the Gibbs measure for the Lipschitz continuous potential. We consider the (suitably normalized) return times of the orbit to the ε-neighborhood of a point z ∈ Ω and prove that for µ-a.e. z the sequence of the normalized return times converges to the Poisson point process in finite dimensional distribution as ε → 0.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 3 , September 1993 , pp. 533 - 556
Copyright
Copyright © Cambridge University Press 1993

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