Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 068, 21 pages      arXiv:1508.03122      https://doi.org/10.3842/SIGMA.2015.068
Contribution to the Special Issue on Algebraic Methods in Dynamical Systems

Dynamics on Wild Character Varieties

Emmanuel Paul a and Jean-Pierre Ramis b
a) Institut de Mathématiques de Toulouse, CNRS UMR 5219, Équipe Émile Picard, Université Paul Sabatier (Toulouse 3), 118 route de Narbonne, 31062 Toulouse CEDEX 9, France
b) Institut de France (Académie des Sciences) and Institut de Mathématiques de Toulouse, CNRS UMR 5219, Équipe Émile Picard, Université Paul Sabatier (Toulouse 3), 118 route de Narbonne, 31062 Toulouse CEDEX 9, France

Received March 26, 2014, in final form August 05, 2015; Published online August 13, 2015

Abstract
In the present paper, we will first present briefly a general research program about the study of the ''natural dynamics'' on character varieties and wild character varieties. Afterwards, we will illustrate this program in the context of the Painlevé differential equations $P_{\rm VI}$ and $P_{\rm V}$.

Key words: character varieties; wild fundamental groupoid; Painlevé equations.

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