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Exponential decay of correlations for surface semi-flows without finite Markov partitions
Author(s):
Viviane
Baladi;
Brigitte
Vallée
Journal:
Proc. Amer. Math. Soc.
133
(2005),
865-874.
MSC (2000):
Primary 37C30, 37D50, 37E35
Posted:
September 29, 2004
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Abstract:
We extend Dolgopyat's bounds on iterated transfer operators to suspensions of interval maps with infinitely many intervals of monotonicity.
References:
- 1.
- N. Anantharaman, Travaux de Dolgopyat sur le mélange des mesures de Gibbs, Chapter 1 of ``Géodésiques fermées d'une surface sous contraintes homologiques,'' unpublished, 2000.
- 2.
- V. Baladi and B. Vallée, Euclidean algorithms are Gaussian, Preprint (2003), www.arxiv.org.
- 3.
- D. Dolgopyat, On decay of correlations in Anosov flows, Ann. of Math., 147, 1998, pp. 357-390. MR 1626749 (99g:58073)
- 4.
- D. Dolgopyat, Private communication (2003).
- 5.
- M. Pollicott, On the mixing of Axiom A attracting flows and a conjecture of Ruelle, Ergodic Theory Dynam. Systems, 19, 1999, pp. 535-548. MR 1685406 (2001d:37038)
- 6.
- M. Pollicott and R. Sharp, Exponential error terms for growth functions on negatively curved surfaces, Amer. J. Math., 120, 1998, pp. 1019-1042. MR 1646052 (99h:58148)
- 7.
- L. Stoyanov, Spectrum of the Ruelle operator and exponential decay of correlations f or open billiard flows, Amer. J. Math., 123, 2001, pp. 715-759. MR 1844576 (2002f:37061)
- 8.
- L.-S. Young, Statistical properties of dynamical systems with some hyperbolicity, Ann. of Math., 147, 1998, pp. 585-650. MR 1637655 (99h:58140)
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Additional Information:
Viviane
Baladi
Affiliation:
CNRS, UMR 7586, Institut de Mathématiques de Jussieu, 75251 Paris, France
Email:
baladi@math.jussieu.fr
Brigitte
Vallée
Affiliation:
CNRS, GREYC, Université de Caen, 14032 Caen, France
Email:
brigitte.vallee@info.unicaen.fr
DOI:
10.1090/S0002-9939-04-07671-3
PII:
S 0002-9939(04)07671-3
Received by editor(s):
November 23, 2003
Posted:
September 29, 2004
Additional Notes:
This work was supported in part by two CNRS MATHSTIC grants. We thank A. Hachemi for a careful reading of a previous version of the paper.
Communicated by:
Michael Handel
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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