Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/2079
Title: Time analysis and entry-exit relation near planar turning points
Authors: DE MAESSCHALCK, Peter 
DUMORTIER, Freddy 
Issue Date: 2005
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Source: JOURNAL OF DIFFERENTIAL EQUATIONS, 215(2). p. 225-267
Abstract: The paper deals with canard solutions at very general turning points of smooth singular perturbation problems in two dimensions. We follow a geometric approach based on the use of C-k-normal forms, centre manifolds and (family) blow up, as we did in (Trans. Amer. Math. Soc., to appear). In (Trans. Amer. Math. Soc., to appear) we considered the existence of manifolds of canard solutions for given appropriate boundary conditions. These manifolds need not be smooth at the turning point. In this paper we essentially study the transition time along such manifolds, as well as the divergence integral, providing a structure theorem for these integrals. As a consequence we get a nice structure theorem for the transition equation, governing the canard solutions. It permits to compare different control manifolds and to obtain a precise description of the entry-exit relation of different canard solutions. Attention is also given to the special case in which the canard manifolds are smooth, i.e. when "formal" canard solutions exist. (c) 2005 Elsevier Inc. All rights reserved.
Notes: Limburgs Univ Ctr, WNI, B-3590 Diepenbeek, Belgium.De Maesschalck, P, Limburgs Univ Ctr, WNI, Univ Campus,Gebouw D, B-3590 Diepenbeek, Belgium.peter.demaesschalck@luc.ac.be freddy.dumortier@luc.ac.be
Keywords: singular perturbation; canard; transition time; entry-exit relation; degenerate turning point; family blow up; centre manifolds; normal forms
Document URI: http://hdl.handle.net/1942/2079
ISSN: 0022-0396
e-ISSN: 1090-2732
DOI: 10.1016/j.jde.2005.01.004
ISI #: 000230069400001
Category: A1
Type: Journal Contribution
Validations: ecoom 2006
Appears in Collections:Research publications

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