Hostname: page-component-6bb9c88b65-6scc2 Total loading time: 0 Render date: 2025-07-24T01:04:56.106Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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