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

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

2005-08-25

arxiv.org/abs/math/0508508v1

Mathematics

Dynamical Systems

36 pages

Scientific paper

We prove the Zorich-Kontsevich conjecture that the non-trivial Lyapunov exponents of the Teichm\"uller 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 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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