Dynamics on Markov surfaces: classification of stationary measures

2024/04/02 by Serge Cantat, Christophe Dupont, Cantat, Serge +3 · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2404.01721

openalex publication_date 2024/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

Consider the four punctured sphere \mathbbS₄². Each choice of four traces, one for each puncture, determines a relative character variety for the representations of the fundamental group of \mathbbS₄² in \sfSL₂(ℂ). We classify the stationary probability measures for the action of the mapping class group \sfMod(\mathbbS₄²) on these character varieties.

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