Limit cycles coming from some uniform isochronous centers
Liang, Haihua (Guangdong Polytechnic Normal University(China). Department of Computer Science)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Fecha:	2016
Resumen:	This article is about the weak 16--th Hilbert problem, i. e. we analyze how many limit cycles can bifurcate from the periodic orbits of a given polynomial differential center when it is perturbed inside a class of polynomial differential systems. More precisely, we consider the uniform isochronous centers \[ x= -y x^2 y (x^2 y^2)^n, y= x x y^2 (x^2 y^2)^n, \] of degree 2n 3 and we perturb them inside the class of all polynomial differential systems of degree 2n 3. For n=0,1 we provide the maximum number of limit cycles, 3 and 8 respectively, that can bifurcate from the periodic orbits of these centers using averaging theory of first order, or equivalently Abelian integrals. For n=2 we show that at least 12 limit cycles can bifurcate from the periodic orbits of the center.
Ayudas:	Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P Ministerio de Economía y Competitividad UNAB13-4E-1604 European Commission 318999 European Commission 316338
Nota:	Agraïments: The first author is supported by the NSF of China (No. 11201086), the Foundation for Distinguished Young Talents in Higher Education of Guangdong, China (No.2012LYM0087) and the Excellent Young Teachers Training Program for colleges and uni- versities of Guangdong Province, China (No. Yq2013107).
Derechos:	Tots els drets reservats.
Lengua:	Anglès
Documento:	Article ; recerca ; Versió acceptada per publicar
Materia:	Averaging theory ; Uniform isochronous centers ; Weak Hilbert problem
Publicado en:	Advanced Nonlinear Studies, Vol. 16 Núm. 2 (2016) , p. 197-220, ISSN 2169-0375

DOI: 10.1515/ans-2015-5010

Postprint 25 p, 401.8 KB

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