2023/12/18 by Ursula Hamenstädt, Hamenstädt, Ursula · 2 citations
Mathematics · #Meromorphic and Entire Functions #Mathematical Dynamics and Fractals #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.48550/arxiv.2312.11656
Let S be a closed oriented surface of genus g≥ 0 with n≥ 0 punctures and 3g-3+n≥ 5. Let Q be a connected component of a stratum in the moduli space Q(S) of area one meromorphic quadratic differentials on S with n simple poles at the punctures or in the moduli space H(S) of abelian differentials on S if n=0. For a compact subset K of Q(S) or of H(S), we show that the asymptotic growth rate of the number of periodic orbits for the Teichmueller flow on Q which are entirely contained in Q-K is at least h(Q)-1 where h(Q)>0 is the complex dimension of Q.