Dynamics in the moduli space of Abelian differentials

Marcelo Viana | Avila, Artur

Keywords: Lyapunov exponent | teichmuller flow | interval exchange map

We announce the proof of the Zorich-Kontsevich conjecture: the non-trivial Lyapunov exponents of the Teichmuller 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 those authors, 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:

• avz0.pdf