Open Access
2007 Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture
Artur Avila, Marcelo Viana
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Acta Math. 198(1): 1-56 (2007). DOI: 10.1007/s11511-007-0012-1


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.

Funding Statement

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


Download Citation

Artur Avila. Marcelo Viana. "Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture." Acta Math. 198 (1) 1 - 56, 2007.


Received: 10 November 2005; Revised: 11 October 2006; Accepted: 11 October 2006; Published: 2007
First available in Project Euclid: 31 January 2017

zbMATH: 1143.37001
MathSciNet: MR2316268
Digital Object Identifier: 10.1007/s11511-007-0012-1

Rights: 2007 © Institut Mittag-Leffler

Vol.198 • No. 1 • 2007
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