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

2007/01/01 by Artur Avila, Marcelo Viana · 152 citations
Mathematics · Physics and Astronomy · #Abelian group #Compact Riemann surface #Conjecture #Foliation (geology) #Geometric and Algebraic Topology #Homology (biology) #Lyapunov exponent #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Moduli space #Pure mathematics #Quantum chaos and dynamical systems #Riemann surface

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

published in Acta Mathematica 198(1), 1-56 (Mittag-Leffler Institute)

openalex publication_date 2007/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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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