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

Artur Avila CNRS UMR 7599, Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie Marcelo Viana IMPA – Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, Brazil

TBD mathscidoc:1701.331979

Acta Mathematica, 198, (1), 1-56, 2005.11
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.
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@inproceedings{artur2005simplicity,
  title={Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture},
  author={Artur Avila, and Marcelo Viana},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203350072017688},
  booktitle={Acta Mathematica},
  volume={198},
  number={1},
  pages={1-56},
  year={2005},
}
Artur Avila, and Marcelo Viana. Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture. 2005. Vol. 198. In Acta Mathematica. pp.1-56. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203350072017688.
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