Dynamics on Markov surfaces: classification of stationary measures

Serge Cantat (1) , Christophe Dupont (1) , Florestan Martin-Baillon (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: representations; random and holomorphic dynamics; stationary and invariant measures

Domaines: Systèmes dynamiques [math.DS]

Serge Cantat, Christophe Dupont, Florestan Martin-Baillon. Dynamics on Markov surfaces: classification of stationary measures. 2024. ⟨hal-04527530⟩