Restricted independence in displacement function for better estimation of cyclicity
Chen, Xingwu (Sichuan University (Xina). Department of Mathematics)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Wang, Zhaoxia (University of Electronic Science and Technology of China. School of Mathematical Sciences)
Zhang, Weinian (Sichuan University (Xina). Department of Mathematics)

Data:	2017
Resum:	Since the independence of focal values is a sufficient condition to give a number of limit cycles arising from a center-focus equilibrium, in this paper we consider a restricted independence to a parametric curve, which gives a method not only to increase the lower bound for the cyclicity of the center-focus equilibrium but also to be available when those focal values are not independent. We apply the method to a nondegenerate cubic center-focus variety and prove that the cyclicity reaches its an upper bound.
Ajuts:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 318999 European Commission 316338 Ministerio de Economía y Competitividad MTM2013-40998-P
Nota:	Agraïments: The author is partially supported by NSFC grant #11471228 (X. Chen), NSFC grant # 11501083 (Z. Wang), and NSFC grants # 11231001 and # 11221101 (W. Zhang).
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Center-focus variety ; Cyclicity ; Focal value ; Independence ; Power sequence
Publicat a:	Journal of differential equations, Vol. 262 (2017) , p. 5773-5791, ISSN 1090-2732

DOI: 10.1016/j.jde.2017.02.015

Postprint 17 p, 792.7 KB

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