The Galoisian envelope of a germ of foliation: the quasi-homogeneous case

Details The Galoisian envelope of a germ of foliation: the quasi-homogeneous case The Galoisian envelope of a germ of foliation: the quasi-homogeneous case

2006-12-11

arxiv.org/abs/math/0612280v1

Mathematics

Dynamical Systems

Scientific paper

We give geometric and algorithmic criterions in order to have of a proper Galois closure for a codimension one germ of quasi-homogeneous foliation. We recall this notion recently introduced by B. Malgrange, and describe the Galois envelope of a group of germs of analytic diffeomorphisms. The geometric criterions are obtained from transverse analytic invariants, whereas the algorithmic ones make use of formal normal forms.

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