Centers and isochronous centers for generalized quintic systems
Giné, Jaume (Universitat de Lleida. Departament de Matemàtica)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)

Date:	2015
Abstract:	In this paper we classify the centers and the isochronous centers of certain polynomial differential systems in R2 of degree d ≥ 5 odd that incomplex notation can be written as z˙ = (λ + i)z + (zz¯)d−52 (Az5 + Bz4z¯ + Cz3z¯2 + Dz2z¯3 + Ezz¯4 + Fz¯5),where λ ∈ R and A, B, C, D, E, F ∈ C. Note that if d = 5 we obtain the full class of polynomial differential systems of the form a linear system with homogeneous polynomial nonlinearities of degree 5. Our study uses algorithms of computational algebra based on the Groebner basis theory and modular arithmetics for simplifying the computations.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2011-22877 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-1204 European Commission 316338 European Commission 318999
Note:	Agraïments: The first author is partially supported by FEDER-UNAB10-4E-378. The third author has been supported by FCT (grant PTDC/MAT/117106/2010 and through CAMGSDgrant number PEst-OE/EEI/LA0009/2013)
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Computation on modular arithmetics ; Gröbner basis theory ; Nondegenerate center
Published in:	Journal of computational and applied mathematics, Vol. 279 (2015) , p. 173-186, ISSN 0377-0427

DOI: 10.1016/j.cam.2014.11.007

Postprint 19 p, 771.0 KB

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