Orbits in Teichmüller dynamics admits a critical exponent gap
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915019619303424 |
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| author | Solan, Omri Nisan |
| author_facet | Solan, Omri Nisan |
| contents | McMullen '03 constructs a collection of orbits $\mathrm{SL}_2(\mathbb{R}).x$ in $\mathcal{H}(1,1)$ with infinitely generated stabilizers $\mathrm{stab}_{\mathrm{SL}_2(\mathbb{R})}(x)$. We prove a gap in the set of critical exponents of stabilizers of $\mathrm{SL}_2(\mathbb{R})$-orbits in $\mathcal{H}_g$: for every $x\in \mathcal{H}_g$, either $\mathrm{stab}_{\mathrm{SL}_2(\mathbb{R})}(x)$ is a lattice, or we have a uniform bound on the critical exponent $δ(\mathrm{stab}_{\mathrm{SL}_2(\mathbb{R})}(x)) \le 1-\varepsilon_g$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09144 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orbits in Teichmüller dynamics admits a critical exponent gap Solan, Omri Nisan Dynamical Systems McMullen '03 constructs a collection of orbits $\mathrm{SL}_2(\mathbb{R}).x$ in $\mathcal{H}(1,1)$ with infinitely generated stabilizers $\mathrm{stab}_{\mathrm{SL}_2(\mathbb{R})}(x)$. We prove a gap in the set of critical exponents of stabilizers of $\mathrm{SL}_2(\mathbb{R})$-orbits in $\mathcal{H}_g$: for every $x\in \mathcal{H}_g$, either $\mathrm{stab}_{\mathrm{SL}_2(\mathbb{R})}(x)$ is a lattice, or we have a uniform bound on the critical exponent $δ(\mathrm{stab}_{\mathrm{SL}_2(\mathbb{R})}(x)) \le 1-\varepsilon_g$. |
| title | Orbits in Teichmüller dynamics admits a critical exponent gap |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2411.09144 |