Dynamics of the Teichmueller flow on compact invariant sets
Dynamical Systems
2010-07-15 v3
Abstract
Let Q(S) be the moduli space of area one holomorphic quadratic differentials for an oriented surface S of genus g with m punctures and 3g-3+m>1. We show that the supremum over all compact subsets K of Q(S) of the asymptotic growth rate of the number of periodic orbits of the Teichmueller flow which are contained in K equals h=6g-6+2m. Moreover, h is also the supremum of the topological entropies of the restriction of the Teichmueller flow to compact invariant subsets of Q(S).
Cite
@article{arxiv.0705.3812,
title = {Dynamics of the Teichmueller flow on compact invariant sets},
author = {Ursula Hamenstaedt},
journal= {arXiv preprint arXiv:0705.3812},
year = {2010}
}