Le groupoïde de Galois de $P\_1$ et son irréductibilité

Details Le groupoïde de Galois de $P\_1$ et son irréductibilité Le groupoïde de Galois de $P\_1$ et son irréductibilité

2005-10-30

arxiv.org/abs/math/0510657v2

Mathematics

Dynamical Systems

34 pages, in french

Scientific paper

In this article, the Galois groupoid of the first Painlev\'{e} equation is computed. This computation use E. Cartan's classification of structural equations of pseudogroups acting on $C^2$ and the degeneration of the first Painlev\'{e} equation on an elliptic equation ($y'' = 6y^2$). A definition of reducibility for singular holomorphic foliations is proposed. A characterisation of reducible foliations on their Galois groupoid is given and applied to prove the foliation irreducibility of the first Painlev\'{e} equation.

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