Dynamics of the Teichmueller flow on compact invariant sets

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).

Final version

References in corpus (3)

• Train tracks and the Gromov boundary of the complex of curves
• Word hyperbolic extensions of surface groups
• Invariant Radon measures on measured lamination space

Cited by in corpus (1)

• Asymptotics of Weil-Petersson geodesics II: bounded geometry and unbounded entropy