Dynamics of the Teichmueller flow on compact invariant sets

Details Dynamics of the Teichmueller flow on compact invariant sets Dynamics of the Teichmueller flow on compact invariant sets

2007-05-25

arxiv.org/abs/0705.3812v3

Mathematics

Dynamical Systems

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Scientific paper

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).

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