uu.seUppsala University Publications

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An improved lower bound on the number of limit cycles bifurcating from a Hamiltonian planar vector field of degree 7PrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2010 (English)In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, Vol. 20, no 5, p. 1451-1458Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

World Scientific Publishing , 2010. Vol. 20, no 5, p. 1451-1458
##### Keyword [en]

Abelian integrals; limit cycles, bifurcation theory, planar Hamiltonian systems, interval analysis
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:uu:diva-107194DOI: 10.1142/S0218127410026599ISI: 000279882400011OAI: oai:DiVA.org:uu-107194DiVA, id: diva2:228185
#####

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Available from: 2009-07-27 Created: 2009-07-27 Last updated: 2017-12-13Bibliographically approved
##### In thesis

The limit cycle bifurcations of a Z(2) equivariant planar Hamiltonian vector field of degree 7 under Z(2) equivariant degree 7 perturbation is studied. We prove that the given system can have at least 53 limit cycles. This is an improved lower bound for the weak formulation of Hilbert's 16th problem for degree 7, i.e. on the possible number of limit cycles that can bifurcate from a degree 7 planar Hamiltonian system under degree 7 perturbation.

1. Computer-aided Computation of Abelian integrals and Robust Normal Forms$(function(){PrimeFaces.cw("OverlayPanel","overlay232942",{id:"formSmash:j_idt781:0:j_idt788",widgetVar:"overlay232942",target:"formSmash:j_idt781:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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