Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/8260
Title: Smoothness of transition maps in singular perturbation problems with one fast variable
Authors: DE MAESSCHALCK, Peter 
Issue Date: 2008
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Source: JOURNAL OF DIFFERENTIAL EQUATIONS, 244(6). p. 1448-1466
Abstract: This paper deals with the smoothness of the transition map between two sections transverse to the fast flow of a singularly perturbed vector field (one fast, multiple slow directions). Orbits connecting both sections are canard orbits, i.e. they first move rapidly towards the attracting part. of a critical surface, then travel a distance near this critical surface, even beyond the point where the orbit enters the repelling part of the critical surface, and finally repel away from the surface. We prove that the transition map is smooth. In a transcritical situation however, where orbits from an attracting part of one critical manifold follow the repelling part of another critical manifold, the smoothness of the transition map may be limited, due to resonance phenomena that are revealed by blowing up the turning point! We present a polynomial example in R-3. (c) 2007 Elsevier Inc. All rights reserved.
Notes: Hasselt Univ, B-3590 Diepenbeek, Belgium.De Maesschalck, P, Hasselt Univ, Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium.peter.demaesschaick@uhasselt.be
Keywords: singular perturbations; entry-exit relation; turning point; blow up; slow-fast systems
Document URI: http://hdl.handle.net/1942/8260
ISSN: 0022-0396
e-ISSN: 1090-2732
DOI: 10.1016/j.jde.2007.10.023
ISI #: 000255005700007
Category: A1
Type: Journal Contribution
Validations: ecoom 2009
Appears in Collections:Research publications

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