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TitleCenters and isochronous centers for generalized quintic systems
Author(s) Jaume Giné, Jaume Llibre, Claudia Valls
TypeArticle in Journal
AbstractAbstract In this paper we classify the centers and the isochronous centers of certain polynomial differential systems in R 2 of degree d ≥ 5 odd that in complex notation are z ̇ = ( λ + i ) z + ( z z ̄ ) d − 5 2 ( A z 5 + B z 4 z ̄ + C z 3 z ̄ 2 + D z 2 z ̄ 3 + E z z ̄ 4 + F z ̄ 5 ) , where z = x + i y , λ ∈ R and A , B , C , D , E , F ∈ C . Note that if d = 5 we obtain the class of polynomial differential systems in the form of a linear system with homogeneous polynomial nonlinearities of degree 5. Due to the huge computations required for computing the necessary and sufficient conditions for the characterization of the centers and isochronous centers, our study uses algorithms of computational algebra based on the Gröbner basis theory and on modular arithmetics.
KeywordsNon-degenerate center, Poincaré–Liapunov–Abel constants, Gröbner basis theory, Computation on modular arithmetics
ISSN0377-0427
URL http://www.sciencedirect.com/science/article/pii/S0377042714004786
LanguageEnglish
JournalJournal of Computational and Applied Mathematics
Volume279
Number0
Pages173 - 186
Year2015
Edition0
Translation No
Refereed No
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