2007/05/25 by Hamenstaedt, Ursula
#30F60 #37A20 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.0705.3812
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).