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Dynamics on Character Varieties and Malgrange irreducibility of Painlevé VI equation

Serge Cantat, Frank Loray (2009)

Annales de l’institut Fourier

We consider representations of the fundamental group of the four punctured sphere into SL ( 2 , ) . The moduli space of representations modulo conjugacy is the character variety. The Mapping Class Group of the punctured sphere acts on this space by symplectic polynomial automorphisms. This dynamical system can be interpreted as the monodromy of the Painlevé VI equation. Infinite bounded orbits are characterized: they come from SU ( 2 ) -representations. We prove the absence of invariant affine structure (and invariant...

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