Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/10786
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dc.contributor.authorDUMORTIER, Freddy-
dc.contributor.authorRoussarie, Robert-
dc.date.accessioned2010-04-01T08:06:46Z-
dc.date.available2010-04-01T08:06:46Z-
dc.date.issued2009-
dc.identifier.citationDiscrete and Continuous Dynamical Systems. Series S, 4. p. 723-781-
dc.identifier.issn1937-1632-
dc.identifier.urihttp://hdl.handle.net/1942/10786-
dc.description.abstractIn this paper we consider singular perturbation problems occuring in planar slow-fast systems ((x) over dot = y - F(x, lambda), (y) over dot = -epsilon G(x, lambda)) where F and are smooth or even real analytic for some results, A is a multiparameter and epsilon is a small parameter. We deal with turning points that are limiting situations of (generalized) Hopf bifurcations and that we call slow-fast Hopf points. We investigate the number of limit cycles that can appear near a slow-fast Hopf point and this under very general conditions. One of the results states that for any analytic family of planar systems, depending on a finite number of parameters, there is a finite upperbound for the number of limit cycles that can bifurcate from a slow-fast Hopf point.The most difficult problem to deal with concerns the uniform treatment of the evolution that a limit cycle undergoes when it grows from a small limit cycle near the singular point to a canard cycle of detectable size. This explains the title of the paper. The treatment, is based on blow-up, good normal forms and appropriate Chebyshev systems. In the paper we also relate the slow-divergence integral as it is used in singular perturbation theory to Abelian integrals that have to be used in studying limit cycles close to the singular point.-
dc.language.isoen-
dc.publisherAMER INST MATHEMATICAL SCIENCES-AIMS-
dc.subject.classification34E17-
dc.subject.otherSlow-fast system-
dc.subject.othersingular perturbation-
dc.subject.otherturning point-
dc.subject.otherHopf bifurcation-
dc.subject.othercanard cycle-
dc.subject.otherLienard equation-
dc.titleBirth of canard cycles-
dc.typeJournal Contribution-
dc.identifier.epage781-
dc.identifier.issue4-
dc.identifier.spage723-
dc.identifier.volume4-
local.bibliographicCitation.jcatA1-
dc.relation.msnMR2552119-
local.publisher.placePO BOX 2604, SPRINGFIELD, MO 65801-2604 USA-
local.type.refereedRefereed-
local.type.specifiedArticle-
local.relation.ispartofseriesnr2-
dc.bibliographicCitation.oldjcatA2-
dc.identifier.doi10.3934/dcdss.2009.2.723-
dc.identifier.isi000498207000002-
dc.identifier.eissn1937-1179-
local.provider.typeWeb of Science-
local.uhasselt.uhpubyes-
item.fulltextNo Fulltext-
item.validationecoom 2021-
item.contributorRoussarie, Robert-
item.contributorDUMORTIER, Freddy-
item.fullcitationDUMORTIER, Freddy & Roussarie, Robert (2009) Birth of canard cycles. In: Discrete and Continuous Dynamical Systems. Series S, 4. p. 723-781.-
item.accessRightsClosed Access-
crisitem.journal.issn1937-1632-
crisitem.journal.eissn1937-1179-
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