On the approximation of the limit cycles function
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 1197 | |
dc.contributor.author | Cherkas, Leonid | |
dc.contributor.author | Grin, Alexander | |
dc.contributor.author | Schneider, Klaus R. | |
dc.date.accessioned | 2016-03-24T17:38:18Z | |
dc.date.available | 2019-06-28T08:02:45Z | |
dc.date.issued | 2007 | |
dc.description.abstract | We consider planar vector fields depending on a real parameter. It is assumed that this vector field has a family of limit cycles which can be described by means of the limit cycles function $l$. We prove a relationship between the multiplicity of a limit cycle of this family and the order of a zero of the limit cycles function. Moreover, we present a procedure to approximate $l(x)$, which is based on the Newton scheme applied to the Poincaré function and represents a continuation method. Finally, we demonstrate the effectiveness of the proposed procedure by means of a Liénard system. The obtained result supports a conjecture by Lins, de Melo and Pugh. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 0946-8633 | |
dc.identifier.uri | https://doi.org/10.34657/2842 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/1911 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | eng |
dc.title | On the approximation of the limit cycles function | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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