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 germ of a vector field with a 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.
Key words and phrases:holomorphic foliation, analytical classification, unfolding of singularities.
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