Analytical moduli for unfoldings of saddle-node vector fields

2007/02/08 by Christiane Rousseau, Rousseau, Christiane, Loïc Teyssier +1
Mathematics · #34A26 #34C20 #4A20 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0702214

openalex publication_date 2007/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider germs of k-parameter generic families of analytic 2-dimensional vector fields unfolding a saddle-node of codimension k and we give a complete modulus of analytic classification under orbital equivalence and a complete modulus of analytic classification under conjugacy. The modulus is an unfolding of the corresponding modulus for the vector field with the saddle-node. The point of view is to compare the family with a "model family" via an equivalence (conjugacy) over canonical sectors. This is done by studying the asymptotic homology of the leaves and its consequences for solutions of the cohomological equation.

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