Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.11530 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912196613636096 |
|---|---|
| author | Tang, Siyuan |
| author_facet | Tang, Siyuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11530 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effective Exponential Drifts on Strata of Abelian Differentials Tang, Siyuan Dynamical Systems 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. |
| title | Effective Exponential Drifts on Strata of Abelian Differentials |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2501.11530 |