WIAS Preprint No. 782, (2002)

Existence and approximation of slow integral manifolds in some degenerate cases



Authors

  • Schneider, Klaus R.
  • Sobolev, Vladimir A.

2010 Mathematics Subject Classification

  • 34C45 34D15 34E15

Keywords

  • singular perturbations, integral manifolds, degenerate cases

Abstract

We consider singularly perturbed differential systems whose degenerate equations have an isolated but not simple solution. In that case, the standard theory to establish a slow integral manifold near this solution does not work. Applying scaling transformations and using the technique of gauge functions we reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can be established by means of the standard theory of singular perturbations. We illustrate our method by several examples.

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