6533b823fe1ef96bd127edbe

RESEARCH PRODUCT

Geometric Singular Perturbation Theory Beyond Normal Hyperbolicity

Freddy DumortierRobert Roussarie

subject

Singular perturbationPhase portraitSingular solutionMathematical analysisPerturbation (astronomy)Vector fieldGravitational singularityCenter manifoldMathematics

description

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.

yearjournalcountryeditionlanguage
2001-01-01
https://doi.org/10.1007/978-1-4613-0117-2_2