The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems

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Título:	The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
Autor/a:	Giacomini, Héctor; Giné, Jaume; Llibre, Jaume
Notas:	In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type centers and consequently the Poincaré–Liapunov method to find linear type centers can be also used to find the nilpotent centers. Moreover, we show that the degenerate centers which are limit of linear type centers are also detectable with the Poincaré–Liapunov method. The second author is partially supported by a DGICYT grant number MTM2005-06098-C02-02 and by a CICYT grant number 2005SGR00550, and by DURSI of Government of Catalonia “Distinció de la Generalitat de Catalunya per a la promoció de la recerca universitària”. The third author is partially supported by a DGICYT grant number MTM2005-06098-C02-01 and by a CICYT grant number 2005SGR00550.
Materia(s):	-Nilpotent center -Degenerate center -Liapunov constants -Cyclicity -Equacions diferencials
Derechos:	(c) Elsevier, 2006
Tipo de documento:	article submittedVersion
Editor:	Elsevier
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