Analytical moduli for unfoldings of saddle-node vector fields
Dynamical Systems
2007-09-03 v3
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.
Cite
@article{arxiv.math/0702214,
title = {Analytical moduli for unfoldings of saddle-node vector fields},
author = {Christiane Rousseau and Loïc Teyssier},
journal= {arXiv preprint arXiv:math/0702214},
year = {2007}
}
Comments
58 pages