Well Adapted Normal Linearization in Singular Perturbation Problems

作者：Bonckaert P; De Maesschalck P; Dumortier F^*

来源：Journal of Dynamics and Differential Equations, 2011, 23(1): 115-139.

DOI：10.1007/s10884-010-9191-0

• Smooth normal linearization
• Vector field
• Line of singularities
• Singular perturbations

We provide smooth local normal forms near singularities that appear in planar singular perturbation problems after application of the well-known family blowup technique. The local normal forms preserve the structure that is provided by the blow-up transformation. 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(infinity) 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) sufficiently small neighborhood of the origin.

• 出版日期2011-3