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Upper bounds for the number of zeroes for some Abelian Integrals
dc.contributor.author | Lázaro Ochoa, José Tomás |
dc.contributor.author | Gasull Embid, Armengol |
dc.contributor.author | Torregrosa, Joan |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2012-01-24T10:31:03Z |
dc.date.available | 2012-01-24T10:31:03Z |
dc.date.created | 2012-01-12 |
dc.date.issued | 2012-01-12 |
dc.identifier.citation | Lázaro, J.; Gasull, A.; Torregrosa, J. "Upper bounds for the number of zeroes for some Abelian Integrals". 2012. |
dc.identifier.uri | http://hdl.handle.net/2117/14763 |
dc.description.abstract | Abstract. 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.extent | 15 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.title | Upper bounds for the number of zeroes for some Abelian Integrals |
dc.type | External research report |
dc.subject.lemac | Funcions abelianes |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.subject.ams | Classificació AMS::34 Ordinary differential equations::34C Qualitative theory |
dc.subject.ams | Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory |
dc.subject.ams | Classificació AMS::41 Approximations and expansions |
dc.rights.access | Open Access |
local.identifier.drac | 9367171 |
dc.description.version | Preprint |
local.citation.author | Lázaro, J.; Gasull, A.; Torregrosa, J. |
local.citation.publicationName | Upper bounds for the number of zeroes for some Abelian Integrals |
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