Analytic normal forms for convergent saddle-node vector fields

2013/07/10 by Schäfke, Reinhard, Teyssier, Loïc Jean Dit
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1307.2840

Abstract

We give unique analytic "normal forms" for germs of a holomorphic vector field of the complex plane in the neighborhood of an isolated singularity of saddle-node type having a convergent formal separatrix. We specifically address the problem of computing the normal form explicitly.

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