Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/1559
Title: Canard solutions at non-generic turning points
Authors: DE MAESSCHALCK, Peter 
DUMORTIER, Freddy 
Issue Date: 2006
Publisher: The American Mathetical Society
Source: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 358(5). p. 2291-2334
Abstract: This paper deals with singular perturbation problems for vector fields on 2-dimensional manifolds. "Canard solutions" are solutions that, starting near an attracting normally hyperbolic branch of the singular curve, cross a "turning point" and follow for a while a normally repelling branch of the singular curve. Following the geometric ideas developed by Dumortier and Roussarie in 1996 for the study of canard solutions near a generic turning point, we study canard solutions near non-generic turning points. Characterization of manifolds of canard solutions is given in terms of boundary conditions, their regularity properties are studied and the relation is described with the more traditional asymptotic approach. It reveals that interesting information on canard solutions can be obtained even in cases where an asymptotic approach fails to work. Since the manifolds of canard solutions occur as intersection of center manifolds defined along respectively the attracting and the repelling branch of the singular curve, we also study their contact and its relation to the "control curve".
Keywords: ingular perturbations; Canard solutions; degenerate turning point;; center manifolds; normal forms; blow up of families; ORDINARY DIFFERENTIAL-EQUATIONS; SINGULAR PERTURBATION-THEORY; MANIFOLDS;
Document URI: http://hdl.handle.net/1942/1559
ISSN: 0002-9947
e-ISSN: 1088-6850
DOI: 10.1090/S0002-9947-05-03839-0
ISI #: 000236172200021
Category: A1
Type: Journal Contribution
Validations: ecoom 2007
Appears in Collections:Research publications

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