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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.

Information

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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References

REFERENCES

[B.]Bowen, R.. Equilibrium states and the ergodic theory of Anosov dmcomorphisms. Springer Lecture Notes in Mathematics 470. Springer, New York, 1975.Google Scholar
[I.T.M.]Ionesco-Tulcea, C. T. & Marinescu, G.. Théorie ergodique pour des classes d'opérations non complàtement continues. Ann. Math. 52 (1950), 140–147.CrossRefGoogle Scholar
[M.]Morita, T.. Random iteration of one-dimensional transformations. Osaka J. Math. 22 (1985), 489–518.Google Scholar
[N.]Nussbaum, R. D.. The radius of the essential spectrum. Duke Math. J. 37 (1970), 473–478.CrossRefGoogle Scholar
[PE.]Petersen, K.. Ergodic Theory. Cambridge University Press, Cambridge, 1983.CrossRefGoogle Scholar
[P.]Pollicott, M.. Meromorphic extensions of generalized zeta functions. Invent. Math. 85 (1986), 147–164.CrossRefGoogle Scholar
[R.I]Ruelle, D.. Thermodynamic formalism. Encyclopedia of Mathematics and its Applications, vol 5, Addison-Wesley, New York, 1978.Google Scholar
[R.II]Ruelle, D.. The thermodynamic formalism for expanding maps. Commun. Math. Phys. 125 (1989), 239–262.CrossRefGoogle Scholar
[S.I]Sinai, Ya. G.. Some mathematical problems in the theory of quantum chaos. Physica A 163 (1990), 197–204.CrossRefGoogle Scholar
[S.II]Sinai, Ya. G.. Mathematical problems in the theory of quantum chaos. Preprint.Google Scholar