Acta Mathematica

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

Artur Avila and Marcelo Viana

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Abstract

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.

Note

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485891882

Digital Object Identifier
doi:10.1007/s11511-007-0012-1

Mathematical Reviews number (MathSciNet)
MR2316268

Zentralblatt MATH identifier
1143.37001

Rights
2007 © Institut Mittag-Leffler

Citation

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. https://projecteuclid.org/euclid.acta/1485891882


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References

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