The Hopf cyclicity of the centers of a class of quintic polynomial vector fields
García, Isaac (Universitat de Lleida. Departament de Matemàtica)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Maza, Susanna (Universitat de Lleida. Departament de Matemàtica)

Date:	2015
Abstract:	We consider families of planar polynomial vector fields having a singularity with purely imaginary eigenvalues for which a basis of its Bautin ideal B is known. We provide an algorithm for computing an upper bound of the Hopf cyclicity less than or equal to the Bautin depth of B. We also present a method for studying the cyclicity problem for the Hamiltonian and the timereversible centers without the necessity of solving previously the Dulac complex center problem associated to the larger complexified family. As application we analyze the Hopf cyclicity of the quintic polynomial family written in complex notation as ˙z = iz+zz¯(Az3+Bz2z¯+Czz¯2+Dz¯3).
Grants:	Ministerio de Economía y Competitividad MTM2011-22877 Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-1204 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999
Note:	Agraïments: FEDER-UNAB10-4E-378
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Bautin ideal ; Cyclicity ; Limit cycles ; Polynomial vector fields
Published in:	Journal of differential equations, Vol. 258 (2015) , p. 1990-2009, ISSN 1090-2732

DOI: 10.1016/j.jde.2014.11.018

Postprint 22 p, 788.6 KB

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