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

2007/01/01 by Artur Avila, Marcelo Viana · 11 citations
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Geometric and Algebraic Topology

paper · pdf · doi:10.1007/s11511-007-0012-1

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.

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