Centers of projective vector fields of spatial quasi-homogeneous systems with weight (m,m,n) and degree 2 on the sphere
Liang, Haihua (Guangdong Polytechnic Normal University(China). Department of Computer Science)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Data:	2016
Resum:	In this paper we study the centers of projective vector fields Q_T of three-dimensional quasi-homogeneous differential system d/dt=Q() with the weight (m,m,n) and degree 2 on the unit sphere S^2. We seek the sufficient and necessary conditions under which Q_T has at least one center on S^2. Moreover, we provide the exact number and the positions of the centers of Q_T. First we give the complete classification of systems d/dt=Q() and then, using the induced systems of Q_T on the local charts of S^2, we determine the conditions for the existence of centers. The results of this paper provide a convenient criterion to find out all the centers of Q_T on S^2 with Q being the quasi-homogeneous polynomial vector field of weight (m,m,n) and degree 2.
Ajuts:	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 Ministerio de Economía y Competitividad UNAB10-4E-378 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568
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. 2012LYM 0087) and the Excellent Young Teachers Training Program for colleges and universities of Guangdong Province, China (No. Yq2013107).
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Projective vector field ; Quasi-homogeneous system ; Sufficient and necessary conditions for centers
Publicat a:	Electronic Journal of Qualitative Theory of Differential Equations, Vol. 103 (2016) , p. 1-26, ISSN 1417-3875

DOI: 10.14232/ejqtde.2016.1.103

Postprint 23 p, 384.6 KB

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