Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 62, No. 4, pp. 531-547 (2005)

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Dynamics in the moduli space of Abelian differentials

Artur Avila and Marcelo Viana

CNRS UMR 7599, Lab. de Probabilités et Modèles Aléatoires, Univ. Pierre et Marie Curie,
Boîte Postale 188, 75252 Paris Cedex 05 -- FRANCE
E-mail: artur@ccr.jussieu.fr
IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro -- BRAZIL
E-mail: viana@impa.br

Abstract: We announce the proof of the Zorich--Kontsevich conjecture: the non-trivial Lyapunov exponents of the Teichmüller flow on (any connected component of a stratum of) the moduli space of Abelian differentials on compact Riemann surfaces are all distinct. By previous work of those authors, this implies the existence of the complete asymptotic Lagrangian flag describing the behavior in homology of the vertical foliation in a typical translation surface.

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Electronic version published on: 7 Mar 2008.

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