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http://hdl.handle.net/1942/1565
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DC Field | Value | Language |
---|---|---|
dc.contributor.author | DUMORTIER, Freddy | - |
dc.contributor.author | Roussarie, R. | - |
dc.date.accessioned | 2007-06-01T11:24:48Z | - |
dc.date.available | 2007-06-01T11:24:48Z | - |
dc.date.issued | 2006 | - |
dc.identifier.citation | JOURNAL OF DIFFERENTIAL EQUATIONS, 227(1). p. 116-165 | - |
dc.identifier.issn | 0022-0396 | - |
dc.identifier.uri | http://hdl.handle.net/1942/1565 | - |
dc.description.abstract | The paper deals with generic perturbations from a Hamiltonian planar vector field and more precisely with the number and bifurcation pattern of the limit cycles. In this paper we show that near a 2-saddle cycle, the number of limit cycles produced in unfoldings with one unbroken connection, can exceed the number of zeros of the related Abelian integral, even if the latter represents a stable elementary catastrophe. We however also show that in general, finite codimension of the Abelian integral leads to a finite upper bound on the local cyclicity. In the treatment, we introduce the notion of simple asymptotic scale deformation. | - |
dc.language.iso | en | - |
dc.publisher | Elsevier | - |
dc.subject.other | Planar vector field; Hamiltonian perturbation; Limit cycle; Abelian integral; Two-saddle cycle; Asymptotic scale deformation | - |
dc.title | Abelian integrals and limit cycles | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 165 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 116 | - |
dc.identifier.volume | 227 | - |
local.bibliographicCitation.jcat | A1 | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.bibliographicCitation.oldjcat | A1 | - |
dc.identifier.doi | 10.1016/j.jde.2005.08.015 | - |
dc.identifier.isi | 000238729700006 | - |
item.accessRights | Closed Access | - |
item.contributor | DUMORTIER, Freddy | - |
item.contributor | Roussarie, R. | - |
item.fulltext | No Fulltext | - |
item.fullcitation | DUMORTIER, Freddy & Roussarie, R. (2006) Abelian integrals and limit cycles. In: JOURNAL OF DIFFERENTIAL EQUATIONS, 227(1). p. 116-165. | - |
item.validation | ecoom 2007 | - |
crisitem.journal.issn | 0022-0396 | - |
crisitem.journal.eissn | 1090-2732 | - |
Appears in Collections: | Research publications |
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