Acta Mathematica

Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture

Artur Avila and Marcelo Viana

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We prove the Zorich–Kontsevich conjecture that the non-trivial Lyapunov exponents of the Teichmüller ow 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 Zorich and Kontsevich, this implies the existence of the complete asymptotic Lagrangian flag describing the behavior in homology of the vertical foliation in a typical translation surface.


Work carried out within the Brazil–France Agreement in Mathematics. Avila is a Clay Research Fellow. Viana is partially supported by Pronex and Faperj.

Article information

Acta Math., Volume 198, Number 1 (2007), 1-56.

Received: 10 November 2005
Revised: 11 October 2006
Accepted: 11 October 2006
First available in Project Euclid: 31 January 2017

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2007 © Institut Mittag-Leffler


Avila, Artur; Viana, Marcelo. Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture. Acta Math. 198 (2007), no. 1, 1--56. doi:10.1007/s11511-007-0012-1.

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