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dc.contributor.authorLázaro Ochoa, José Tomás
dc.contributor.authorGasull Embid, Armengol
dc.contributor.authorTorregrosa, Joan
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.date.accessioned2012-01-24T10:31:03Z
dc.date.available2012-01-24T10:31:03Z
dc.date.created2012-01-12
dc.date.issued2012-01-12
dc.identifier.citationLázaro, J.; Gasull, A.; Torregrosa, J. "Upper bounds for the number of zeroes for some Abelian Integrals". 2012.
dc.identifier.urihttp://hdl.handle.net/2117/14763
dc.description.abstractAbstract. Consider the vector field x0 = -yG(x, y), y0 = 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 which is 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 in 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.extent15 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshFunctions, Abelian
dc.titleUpper bounds for the number of zeroes for some Abelian Integrals
dc.typeExternal research report
dc.subject.lemacFuncions abelianes
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.subject.amsClassificació AMS::34 Ordinary differential equations::34C Qualitative theory
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
dc.subject.amsClassificació AMS::41 Approximations and expansions
dc.rights.accessOpen Access
local.identifier.drac9367171
dc.description.versionPreprint
local.citation.authorLázaro, J.; Gasull, A.; Torregrosa, J.
local.citation.publicationNameUpper bounds for the number of zeroes for some Abelian Integrals


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