arXiv subjects
Publications and source records attributed to Serge Cantat.
We study the monodromy of Painlevé VI equation from a dynamical point of view. This is applied to the description of bounded orbits, and to a proof of the irreducibility of Painlevé VI equation in the sens of Casale and Malgrange. On our way, we compute the entropy of each element of the monodromy group, and we precise the dictionary between character varieties and Painlevé equations.
We study the dynamics of mapping class groups on 2-dimensional character varieties. We shall show that the dynamics of pseudo-Anosov mapping classes resembles in many ways the dynamics of Hénon mappings, and then apply this idea to answer open questions concerning the geometry of discrete and faithful representations, Painlevé sixth equation, and discrete Schroedinger operators.
Numerical estimates are given for the spectral radius of simple random walks on Cayley graphs. Emphasis is on the case of the fundamental group of a closed surface, for the usual system of generators.