2025/01/20 by Si‐Yuan Tang, Tang, Siyuan
Mathematics · Computer Science · #advanced mathematical theories #Advanced Mathematical Modeling in Engineering #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2501.11530
We study the dynamics of SL2(ℝ) on the stratum of translation surfaces H(2). In particular, we prove that an orbit of the upper triangular subgroup of SL2(ℝ) has a discretized dimension of almost 1 in a direction transverse to the SL2(ℝ)-orbit. The proof proceeds via an effective closing lemma, and the Margulis function technique, which serves as an effective version of the exponential drift on H(2). The idea is based on the use of McMullen's classification theorem, together with Lindenstrauss-Mohammadi-Wang's effective equidistribution theorems in homogeneous dynamics.