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Upper bounds for the number of zeroes for some Abelian integrals
dc.contributor.author | Gasull Embid, Armengol |
dc.contributor.author | Lázaro Ochoa, José Tomás |
dc.contributor.author | Torregrosa, Joan |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2012-10-08T10:08:30Z |
dc.date.created | 2012-09 |
dc.date.issued | 2012-09 |
dc.identifier.citation | Gasull, A.; Lázaro, J.T.; Torregrosa, J. Upper bounds for the number of zeroes for some Abelian integrals. "Nonlinear analysis, theory, methods and applications", Setembre 2012, vol. 75, núm. 13, p. 5169-5179. |
dc.identifier.issn | 0362-546X |
dc.identifier.uri | http://hdl.handle.net/2117/16667 |
dc.description.abstract | Consider the vector field x′=−yG(x,y),y′=xG(x,y), where the set of critical points {G(x,y)=0} is formed by K straight lines, not passing through the origin and parallel to one or two orthogonal directions. We perturb it with a general polynomial perturbation of degree n and study the maximum number of limit cycles that can bifurcate from the period annulus of the origin in terms of K and n. Our approach is based on the explicit computation of the Abelian integral that controls the bifurcation and on a new result for bounding the number of zeroes of a certain family of real functions. When we apply our results for K≤4 we recover or improve some results obtained in several previous works. |
dc.format.extent | 11 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.lcsh | Functions, Abelian |
dc.subject.other | Abelian integrals |
dc.subject.other | Chebyshev system |
dc.subject.other | Limit cycles |
dc.subject.other | Number of zeroes of real functions |
dc.subject.other | Weak 16th Hilbert's Problem |
dc.title | Upper bounds for the number of zeroes for some Abelian integrals |
dc.type | Article |
dc.subject.lemac | Equacions diferencials ordinàries |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.identifier.doi | 10.1016/j.na.2012.04.033 |
dc.description.peerreviewed | Peer Reviewed |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 10652694 |
dc.description.version | Postprint (published version) |
dc.date.lift | 10000-01-01 |
local.citation.author | Gasull, A.; Lázaro, J.T.; Torregrosa, J. |
local.citation.publicationName | Nonlinear analysis, theory, methods and applications |
local.citation.volume | 75 |
local.citation.number | 13 |
local.citation.startingPage | 5169 |
local.citation.endingPage | 5179 |
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