Effective Exponential Drifts on Strata of Abelian Differentials

Siyuan Tang

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arXiv · 2501.11530

Effective Exponential Drifts on Strata of Abelian Differentials

Siyuan Tang

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Abstract

We study the dynamics of $SL_{2}(\mathbb{R})$ on the stratum of translation surfaces $\mathcal{H}(2)$. In particular, we prove that an orbit of the upper triangular subgroup of $SL_{2}(\mathbb{R})$ has a discretized dimension of almost $1$ in a direction transverse to the $SL_{2}(\mathbb{R})$-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 $\mathcal{H}(2)$. The idea is based on the use of McMullen's classification theorem, together with Lindenstrauss-Mohammadi-Wang's effective equidistribution theorems in homogeneous dynamics.

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BibTeX RIS

Siyuan Tang. 2025-01-20. Effective Exponential Drifts on Strata of Abelian Differentials. https://arxiv.org/abs/2501.11530

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