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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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