Holomorphic dynamics, Painlev\'e VI equation and Character Varieties
Dynamical Systems
2007-12-05 v2 Algebraic Geometry
Classical Analysis and ODEs
Abstract
We study the monodromy of Painlev\'e 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 Painlev\'e 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 Painlev\'e equations.
Cite
@article{arxiv.0711.1579,
title = {Holomorphic dynamics, Painlev\'e VI equation and Character Varieties},
author = {Serge Cantat and Frank Loray},
journal= {arXiv preprint arXiv:0711.1579},
year = {2007}
}