Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4638644 | Journal of Computational and Applied Mathematics | 2015 | 14 Pages |
Abstract
In this paper we classify the centers and the isochronous centers of certain polynomial differential systems in R2R2 of degree d≥5d≥5 odd that in complex notation are ż=(λ+i)z+(zz̄)d−52(Az5+Bz4z̄+Cz3z̄2+Dz2z̄3+Ezz̄4+Fz̄5), where z=x+iyz=x+iy, λ∈Rλ∈R and A,B,C,D,E,F∈CA,B,C,D,E,F∈C. Note that if d=5d=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
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Jaume Giné, Jaume Llibre, Claudia Valls,