WIAS Preprint No. 782, (2002)

Existence and approximation of slow integral manifolds in some degenerate cases


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

2010 Mathematics Subject Classification

  • 34C45 34D15 34E15


  • singular perturbations, integral manifolds, degenerate cases




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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