Dynamics on Markov surfaces: classification of stationary measures
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916189222993920 |
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| author | Cantat, Serge Dupont, Christophe Martin-Baillon, Florestan |
| author_facet | Cantat, Serge Dupont, Christophe Martin-Baillon, Florestan |
| contents | Consider the four punctured sphere ${\mathbb{S}}_4^2$. Each choice of four traces, one for each puncture, determines a relative character variety for the representations of the fundamental group of ${\mathbb{S}}_4^2$ in ${\sf{SL}}_2(\mathbb{C})$. We classify the stationary probability measures for the action of the mapping class group ${\sf{Mod}}({\mathbb{S}}_4^2)$ on these character varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01721 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamics on Markov surfaces: classification of stationary measures Cantat, Serge Dupont, Christophe Martin-Baillon, Florestan Dynamical Systems Consider the four punctured sphere ${\mathbb{S}}_4^2$. Each choice of four traces, one for each puncture, determines a relative character variety for the representations of the fundamental group of ${\mathbb{S}}_4^2$ in ${\sf{SL}}_2(\mathbb{C})$. We classify the stationary probability measures for the action of the mapping class group ${\sf{Mod}}({\mathbb{S}}_4^2)$ on these character varieties. |
| title | Dynamics on Markov surfaces: classification of stationary measures |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2404.01721 |