Holomorphic dynamics, Painlevé VI equation and Character Varieties

Serge Cantat; Frank Loray

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arXiv · 0711.1579

Holomorphic dynamics, Painlevé VI equation and Character Varieties

Serge Cantat·Frank Loray

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Abstract

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.

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Serge Cantat, Frank Loray. 2007-12-05. Holomorphic dynamics, Painlevé VI equation and Character Varieties. https://arxiv.org/abs/0711.1579

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