Effective density of surfaces near Teichmüller curves

2024/11/05 by Tang, Siyuan
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.03560

Abstract

We study the dynamics of SL₂(ℝ) on the stratum of translation surfaces H(2). Especially, we obtain effective density theorems on H(2) for orbits of the upper triangular subgroup P of SL₂(ℝ) with the based surfaces near a small Teichmüller curve. The proof is based on the use of McMullen's classification theorem, together with the effective equidistribution theorems in homogeneous dynamics. In particular, we compare the P-orbit of a surface, and the P-orbit of its absolute periods using the Lindenstrauss-Mohammadi-Wang's effective equidistribution theorem.

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