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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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