www.uhasselt.be
DSpace

Document Server@UHasselt >
Research >
Research publications >

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
Citation: 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".
URI: http://hdl.handle.net/1942/1559
DOI: 10.1090/S0002-9947-05-03839-0
ISI #: 000236172200021
ISSN: 0002-9947
Category: A1
Type: Journal Contribution
Validation: ecoom, 2007
Appears in Collections: Research publications

Files in This Item:

Description SizeFormat
Postprint399.35 kBAdobe PDF

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.