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A large deviations bound for the Teichmüller flow on the moduli space of abelian differentials

Published online by Cambridge University Press:  20 July 2010

VÍTOR ARAÚJO  and
ALEXANDER I. BUFETOV
VÍTOR ARAÚJO
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, C.P. 68.530, 21.945-970 Rio de Janeiro, RJ, Brazil (email: [email protected])
ALEXANDER I. BUFETOV
Affiliation:
Department of Mathematics, Rice University, MS 136, 6100 Main Street, Houston, Texas 77251-1892, USA The Steklov Institute of Mathematics, Russian Academy of Sciences, Gubkina str. 8, 119991 Moscow, Russia (email: [email protected], [email protected])
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Abstract

Large deviation rates are obtained for suspension flows over symbolic dynamical systems with a countable alphabet. We use a method employed previously by the first author [Large deviations bound for semiflows over a non-uniformly expanding base. Bull. Braz. Math. Soc. (N.S.)38(3) (2007), 335–376], which follows that of Young [Some large deviation results for dynamical systems. Trans. Amer. Math. Soc.318(2) (1990), 525–543]. As a corollary of the main results, we obtain a large deviation bound for the Teichmüller flow on the moduli space of abelian differentials, extending earlier work of Athreya [Quantitative recurrence and large deviations for Teichmuller geodesic flow. Geom. Dedicata119 (2006), 121–140].

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 4 , August 2011 , pp. 1043 - 1071
Copyright
Copyright © Cambridge University Press 2010

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