Analytical and formal classifications of quasi-homogeneous foliations in C^2

Yohann Genzmer (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We prove a result of classification for germs of formal and convergent quasi-homogeneous foliations in C 2 with fixed separatrix. Basically, we prove that the analytical and formal class of such a foliation depend respectively only on the analytical and formal class of its representation of projective holonomy.

Mots clés: Dynamical system; Holomorphic foliations; Singularities

Domaines: Variables complexes [math.CV]; Systèmes dynamiques [math.DS]

Yohann Genzmer. Analytical and formal classifications of quasi-homogeneous foliations in C^2. Journal of Differential Equations, 2008, 245 (6), pp.1656-1680. ⟨hal-01823873⟩