Well adapted normal linearization in singular perturbation problems

We provide smooth local normal forms near singularities that appear in planar singular perturbation problems after application of the well-known family blow up technique. The local normal forms preserve the structure that is provided by the blow-up ransformation. In a similar context, C^k-structure-preserving normal forms were shown to exist, for any finite k. In this paper, we improve the smoothness by showing the existence of a C^\infty normalizing transformation, or in other cases by showing the existence of a single normalizing transformation that is C^k for each k, provided one restricts the singular parameter epsilon to a (k-dependent) suffiiently small neighborhood of the origin.

Jaar van publicatie:2011

Trefwoorden:smooth normal linearization, vector field, line of singularities, singular perturbations

BOF-keylabel:ja

IOF-keylabel:ja

BOF-publication weight:3

CSS-citation score:1

Authors from:Higher Education

Toegankelijkheid:Open