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Decay of correlations for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations and the central limit theorem for the Teichmüller flow on the moduli space of Abelian differentials


Author: Alexander I. Bufetov
Journal: J. Amer. Math. Soc. 19 (2006), 579-623
MSC (2000): Primary 37A25, 37F25, 37F30, 37E05, 60F05, 60J10
DOI: https://doi.org/10.1090/S0894-0347-06-00528-5
Published electronically: February 22, 2006
MathSciNet review: 2220100
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Abstract | References | Similar Articles | Additional Information

Abstract: The aim of this paper is to prove a stretched-exponential bound for the decay of correlations for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations. A corollary is the Central Limit Theorem for the Teichmüller flow on the moduli space of abelian differentials with prescribed singularities.


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Additional Information

Alexander I. Bufetov
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Address at time of publication: (Until June 30, 2006) Department of Mathematics, The University of Chicago, 5734 South University Avenue, Chicago, Illinois 60637; (starting July 1, 2006) Department of Mathematics, Rice University, MS 136, 6100 Main Street, Houston, Texas 77251-1892
Email: bufetov@math.rice.edu

DOI: https://doi.org/10.1090/S0894-0347-06-00528-5
Keywords: Interval exchange transformations, Rauzy induction, speed of mixing, Teichm{\"u}ller geodesic flow, central limit theorem.
Received by editor(s): October 6, 2004
Published electronically: February 22, 2006
Dedicated: Se non quel tanto che n’accende il sole. Michelangelo Buonarroti
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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