95 research outputs found
Volumes of strata of Abelian differentials and Siegel-Veech constants in large genera
We state conjectures on the asymptotic behavior of the volumes of moduli
spaces of Abelian differentials and their Siegel-Veech constants as genus tends
to infinity. We provide certain numerical evidence, describe recent advances
and the state of the art towards proving these conjectures.Comment: Some background material is added on request of the referee. To
appear in Arnold Math. Journa
Semisimplicity of the Lyapunov spectrum for irreducible cocycles
Let be a semisimple Lie group acting on a space , let be a
compactly supported measure on , and let be a strongly irreducible
linear cocycle over the action of . We then have a random walk on , and
let be the associated shift map. We show that the cocycle over the
action of is conjugate to a block conformal cocycle.
This statement is used in the recent paper by Eskin-Mirzakhani on the
classifications of invariant measures for the SL(2,R) action on moduli space.
The ingredients of the proof are essentially contained in the papers of
Guivarch and Raugi and also Goldsheid and Margulis.Comment: 27 pages. Final version based on the referee's report. To appear in
Israel J. Mat
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