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

Marcelo Viana | Avila, Artur

Keywords: Lyapunov exponent | teichmuller flow | interval exchange map

We prove the Zorich-Kontsevich conjecture that the non-trivial Lyapunov exponents of the Teichmúller 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.

Anexos:

• avz2.pdf