Holomorphic dynamics, Painlevé VI equation and Character Varieties

Details Holomorphic dynamics, Painlevé VI equation and Character Varieties Holomorphic dynamics, Painlevé VI equation and Character Varieties

2007-11-10

arxiv.org/abs/0711.1579v2

Mathematics

Dynamical Systems

Scientific paper

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.

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