Geometric Singular Perturbation Theory Beyond Normal Hyperbolicity

  • Freddy Dumortier
  • Robert Roussarie
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 122)


Geometric Singular Perturbation theory has traditionally dealt only with perturbation problems near normally hyperbolic manifolds of singularities. In this paper we want to show how blow up techniques can permit enlarging the applicability to non-normally hyperbolic points. We will present the method on well chosen examples in the plane and in 3-space.


Vector Field Phase Portrait Singular Perturbation Center Manifold Singular Perturbation Problem 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Freddy Dumortier
    • 2
  • Robert Roussarie
    • 1
  1. 1.Laboratoire de Topologie, CNRS-UMR5584, U.F.R. Sciences et TechniquesUniversité de BourgogneDijon CedexFrance
  2. 2.Limburgs Universitair CentrumDiepenbeekBelgium

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