The period function of generalized Loud's centers
Marín Pérez, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)

Date:	2013
Abstract:	In this paper a three parameter family of planar differential systems with homogeneous nonlinearities of arbitrary odd degree is studied. This family is an extension to higher degree of the Loud's systems. The origin is a nondegenerate center for all values of the parameter and we are interested in the qualitative properties of its period function. We study the bifurcation diagram of this function focusing our attention on the bifurcations occurring at the polycycle that bounds the period annulus of the center. Moreover we determine some regions in the parameter space for which the corresponding period function is monotonous or it has at least one critical period, giving also its character (maximum or minimum). Finally we propose a complete conjectural bifurcation diagram of the period function of these generalized Loud's centers.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 Ministerio de Economía y Competitividad MTM2008-03437
Note:	Agraïments: The first author is partially supported by the DGES/FEDER grant MTM2011-26674-C02-01.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Period function ; Desingularization ; Critical period ; Bifurcation
Published in:	Journal of differential equations, Vol. 255 (2013) , p. 3071-3097, ISSN 1090-2732

DOI: 10.1016/j.jde.2013.07.025

Postprint 26 p, 700.8 KB

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