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arXiv · 2404.01721

Dynamics on Markov surfaces: classification of stationary measures

Serge Cantat·Christophe Dupont·Florestan Martin-Baillon
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Abstract

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.

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Serge Cantat, Christophe Dupont, Florestan Martin-Baillon. 2024-04-02. Dynamics on Markov surfaces: classification of stationary measures. https://arxiv.org/abs/2404.01721

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