Effective density of surfaces near Teichmüller curves
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916616423342080 |
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| author | Tang, Siyuan |
| author_facet | Tang, Siyuan |
| contents | We study the dynamics of $SL_{2}(\mathbb{R})$ on the stratum of translation surfaces $\mathcal{H}(2)$. Especially, we obtain effective density theorems on $\mathcal{H}(2)$ for orbits of the upper triangular subgroup $P$ of $SL_{2}(\mathbb{R})$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03560 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Effective density of surfaces near Teichmüller curves Tang, Siyuan Dynamical Systems We study the dynamics of $SL_{2}(\mathbb{R})$ on the stratum of translation surfaces $\mathcal{H}(2)$. Especially, we obtain effective density theorems on $\mathcal{H}(2)$ for orbits of the upper triangular subgroup $P$ of $SL_{2}(\mathbb{R})$ 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. |
| title | Effective density of surfaces near Teichmüller curves |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2411.03560 |