Details:
Title  Centers and isochronous centers for generalized quintic systems  Author(s)  Jaume Giné, Jaume Llibre, Claudia Valls  Type  Article in Journal  Abstract  Abstract 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.  Keywords  Nondegenerate center, Poincaré–Liapunov–Abel constants, Gröbner basis theory, Computation on modular arithmetics  ISSN  03770427 
URL 
http://www.sciencedirect.com/science/article/pii/S0377042714004786 
Language  English  Journal  Journal of Computational and Applied Mathematics  Volume  279  Number  0  Pages  173  186  Year  2015  Edition  0  Translation 
No  Refereed 
No 
