A geometric criterion for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle

Details A geometric criterion for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle A geometric criterion for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle

2010-09-23

arxiv.org/abs/1009.4655v2

Mathematics

Dynamical Systems

46 pages

Scientific paper

We prove a geometric criterion on a $\SL$-invariant ergodic probability measure on the moduli space of holomorphic abelian differentials on Riemann surfaces for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle on the real Hodge bundle. Applications include measures supported on the $\SL$-orbits of all algebraically primitive Veech surfaces (see also \cite{Bouw:Moeller}) and of all Prym eigenforms discovered in \cite{McMullen2}, as well as all canonical absolutely continuous measures on connected components of strata of the moduli space of abelian differentials (see also \cite{Ftwo}, \cite{Avila:Viana}). The argument simplifies and generalizes our proof for the case of canonical measures \cite{Ftwo}. In an Appendix Carlos Matheus discusses several relevant examples which further illustrate the power and the limitations of our criterion.

Affiliated with

Also associated with

No associations

Rating

A geometric criterion for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A geometric criterion for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A geometric criterion for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-339215