Simultaneous bifurcation of limit cycles from a linear center with extra singular points
Pérez-González, Set (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2014
Abstract:	The period annuli of the planar vector field x' = −yF(x, y), y' = xF(x, y), where the set {F(x, y) = 0} consists of k different isolated points, is defined by k + 1 concentric annuli. In this paper we perturb it with polynomials of degree n and we study how many limit cycles bifurcate, up to a first order analysis, from all the period annuli simultaneously in terms of k and n. Additionally, we prove that the associated Abelian integral is piecewise rational and, when k = 1, the provided upper bound is reached. Finally, the case k = 2 is also treated.
Grants:	Ministerio de Ciencia e Innovación MTM 2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Polynomial perturbation of centers ; Piecewise rational abelian integral ; Simultaneity of limit cycles from several period annuli
Published in:	Bulletin des Sciences Mathematiques, Vol. 138 (2014) , p. 124-138, ISSN 0007-4497

DOI: 10.1016/j.bulsci.2013.09.004

Postprint 15 p, 373.1 KB

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