Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/2453
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dc.contributor.authorDUMORTIER, Freddy-
dc.contributor.authorLi, CZ-
dc.date.accessioned2007-11-14T10:44:58Z-
dc.date.available2007-11-14T10:44:58Z-
dc.date.issued2003-
dc.identifier.citationJOURNAL OF DIFFERENTIAL EQUATIONS, 188(2). p. 512-554-
dc.identifier.issn0022-0396-
dc.identifier.urihttp://hdl.handle.net/1942/2453-
dc.description.abstractThe paper deals with Lienard equations of the form <(x)over dot>= y, <(y) over dot>= P(x) + yQ(x) with P and Q polynomials of degree, respectively, 3 and 2. Attention goes to perturbations of the Hamiltonian vector fields with an elliptic Hamiltonian of degree four, exhibiting a figure eight-loop. It is proved that the least upper bound of the number of zeros of the related elliptic integral is five, and this is a sharp bound, multiplicity taken into account. Moreover, if restricting to the level curves "inside" a saddle loop or "outside" the figure eight-loop the sharp upper bound is respectively two or four; also the multiplicity of the zeros is at most four. This is the last one in a series of papers on this subject. The results of this paper, together with (J. Differential Equations 176 (2001) 114; J. Differential Equations 175 (2001) 209; J. Differential Equations, to be published), largely finish the study of the cubic perturbations of the elliptic Hamiltonians of degree four and presumably provide a complete description of the number and the possible configurations of limit cycles for cubic Lienard equations with small quadratic damping. As a special case, we obtain a configuration of four limit cycles surrounding three singularities together with a "small" limit cycle which surrounds one of the singularities. (C) 2002 Elsevier Science (USA). All rights reserved.-
dc.language.isoen-
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE-
dc.titlePerturbation from an elliptic Hamiltonian of degree four - IV figure eight-loop-
dc.typeJournal Contribution-
dc.identifier.epage554-
dc.identifier.issue2-
dc.identifier.spage512-
dc.identifier.volume188-
local.format.pages43-
local.bibliographicCitation.jcatA1-
dc.description.notesLimburgs Univ Ctr, B-3590 Diepenbeek, Belgium. Peking Univ, Dept Math, Beijing 100871, Peoples R China.Dumortier, F, Limburgs Univ Ctr, Univ Campus, B-3590 Diepenbeek, Belgium.-
local.type.refereedRefereed-
local.type.specifiedArticle-
dc.bibliographicCitation.oldjcatA1-
dc.identifier.doi10.1016/S0022-0396(02)00111-0-
dc.identifier.isi000180988300007-
item.fulltextNo Fulltext-
item.validationecoom 2004-
item.contributorDUMORTIER, Freddy-
item.contributorLi, CZ-
item.fullcitationDUMORTIER, Freddy & Li, CZ (2003) Perturbation from an elliptic Hamiltonian of degree four - IV figure eight-loop. In: JOURNAL OF DIFFERENTIAL EQUATIONS, 188(2). p. 512-554.-
item.accessRightsClosed Access-
crisitem.journal.issn0022-0396-
crisitem.journal.eissn1090-2732-
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