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

Bufetov, Alexander^1, 2

¹ Department of Mathematics, Princeton University, Princeton, New Jersey 08544
² (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

Journal of the American Mathematical Society, Tome 19 (2006) no. 3, pp. 579-623

Résumé

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.

Détail

DOI : 10.1090/S0894-0347-06-00528-5

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