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.