Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/41982
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dc.contributor.authorDE MAESSCHALCK, Peter-
dc.contributor.authorTorregrosa, Joan-
dc.date.accessioned2024-01-03T09:57:08Z-
dc.date.available2024-01-03T09:57:08Z-
dc.date.issued2024-
dc.date.submitted2024-01-03T09:47:24Z-
dc.identifier.citationJournal of Differential Equations, 380 , p. 181 -197-
dc.identifier.urihttp://hdl.handle.net/1942/41982-
dc.description.abstractprovide the best lower bound for the number of critical periods of planar polynomial centers known up to now. The new lower bound is obtained in the Hamiltonian class and considering a single period annulus. This lower bound doubles the previous one from the literature, and we end up with at least n2 - 2 (resp. n2 - 2n - 1) critical periods for planar polynomial systems of odd (resp. even) degree n. Key idea is the perturbation of a vector field with many cusp equilibria, whose construction is by itself a nontrivial construction that uses elements of catastrophe theory.(c) 2023 Elsevier Inc. All rights reserved.-
dc.description.sponsorshipThis work has been realized thanks to the Spanish AEI PID2019-104658GB-I00 grant; the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&M CEX2020-001084-M grant; and the Catalan AGAUR 2021SGR00113 grant. Support was also received through FWO-NSFC bilateral grant G0F1822N. We would like to thank the kind hospitality of the research team of Universitat de les Illes Balears who gave us the opportunity to work together for this work. This project was mainly carried out during a research visit of both authors to UIB. We would like to thank Armengol Gasull for his helpful discussions in some moments during the development of the work.-
dc.language.isoen-
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE-
dc.rights2023 Elsevier Inc. All rights reserved.-
dc.subject.otherCritical periods-
dc.subject.otherHamiltonian vector fields-
dc.subject.otherBest lower bound-
dc.subject.otherDegree n vector field-
dc.titleCritical periods in planar polynomial centers near a maximum number of cusps-
dc.typeJournal Contribution-
dc.identifier.epage197-
dc.identifier.spage181-
dc.identifier.volume380-
local.format.pages17-
local.bibliographicCitation.jcatA1-
dc.description.notesDe Maesschalck, P (corresponding author), Hasselt Univ, Campus Diepenbeek,Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium.-
dc.description.notespeter.demaesschalck@uhasselt.be; joan.torregrosa@uab.cat-
local.publisher.place525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA-
local.type.refereedRefereed-
local.type.specifiedArticle-
dc.identifier.doi10.1016/j.jde.2023.10.034-
dc.identifier.isi001110106000001-
dc.contributor.orcidTorregrosa, Joan/0000-0002-2753-1827-
local.provider.typewosris-
local.description.affiliation[De Maesschalck, Peter] Hasselt Univ, Campus Diepenbeek,Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium.-
local.description.affiliation[Torregrosa, Joan] Univ Autonoma Barcelona, Dept Matematiques, Bellaterra 08193, Barcelona, Spain.-
local.description.affiliation[Torregrosa, Joan] Ctr Recerca Matemat, Campus Bellaterra, Bellaterra 08193, Barcelona, Spain.-
local.uhasselt.internationalyes-
item.fulltextWith Fulltext-
item.accessRightsEmbargoed Access-
item.embargoEndDate2024-07-25-
item.fullcitationDE MAESSCHALCK, Peter & Torregrosa, Joan (2024) Critical periods in planar polynomial centers near a maximum number of cusps. In: Journal of Differential Equations, 380 , p. 181 -197.-
item.contributorDE MAESSCHALCK, Peter-
item.contributorTorregrosa, Joan-
crisitem.journal.issn0022-0396-
crisitem.journal.eissn1090-2732-
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