Dynamics of groups of automorphisms of character varieties and Fatou/Julia decomposition for Painlevé 6

Julio Rebelo, Roland Roeder

We study the dynamics of the group of holomorphic automorphisms of the affine cubic surfaces \begin{align*} S_{A,B,C,D} = \{(x,y,z) \in \mathbb{C}^3 \, : \, x^2 + y^2 + z^2 +xyz =…