Normal forms of topologically quasi-homogeneous foliations on (\C²,0)

2013/09/05 by Truong Hong Minh, Minh, Truong Hong
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DS

paper · pdf · doi:10.48550/arxiv.1309.1411

18 pages

arxiv created 2013/09/05 · openalex publication_date 2013/09/05 · arxiv updated 2013/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to construct formal normal forms for the class of topologically quasi-homogeneous foliations under generic conditions. Any such normal form is given as the sum of three terms: an initial generic quasi-homogeneous term, a hamiltonian term and a radial term. Moreover, we also show that the number of free coefficients in the hamiltonian part is consistent with the dimension of Mattei's moduli space of unfoldings.

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