Centers and isochronous centers for two classes of generalized seventh and ninth systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Instituto Superior Técnico. Departamento de Matemática (Portugal))

Date:	2010
Abstract:	We classify new classes of centers and of isochronous centers for polynomial differential systems in R2 of arbitrary odd degree d ≥ 7 that in complex notation z = x + iy can be written as z˙=(λ+i)z+(zz)d-7-2j/2 (Az5+jz2+j+Bz4+jz3+j+Cz3+jz4+j+Dz7+2j), where j is either 0 or 1, λ ∈ R and A,B,C ∈ C. Note that if j = 0 and d = 7 we obtain a special case of seventh polynomial differential systems which can have a center at the origin, and if j = 1 and d = 9 we obtain a special case of ninth polynomial differential systems which can have a center at the origin.
Grants:	Ministerio de Ciencia y Tecnología MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2005/SGR-00550
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Published in:	Journal of dynamics and differential equations, Vol. 22, Issue 4 (December 2010) , p. 657-675, ISSN 1572-9222

DOI: 10.1007/s10884-010-9175-0

Postprint 22 p, 801.7 KB

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