Centers and isochronous centers for generalized quintic systems
In this paper we classify the centers and the isochronous centers of certain polynomial differential systems in R2 of degree d≥5 odd that in complex notation are ż=(λ+i)z(zz̄)d−52(Az5+Bz4z̄+Cz3z̄2+Dz2z̄3+Ezz̄4+Fz̄5), where z=x+iy λ∈R and A,B,C,D,E,F∈C. Note that if d=5 we obtain the class of polyno...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2015 |
| País: | España |
| Recursos: | Universitat de Lleida (UdL) |
| Repositorio: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/58410 |
| Acesso em linha: | https://doi.org/10.1016/j.cam.2014.11.007 http://hdl.handle.net/10459.1/58410 |
| Access Level: | acceso abierto |
| Palavra-chave: | Non–degenerate center Poincaré-Liapunov-Abel constants Gröbner basis theory Computation on modular arithmetics Matemàtica Mathematics |
| Resumo: | In this paper we classify the centers and the isochronous centers of certain polynomial differential systems in R2 of degree d≥5 odd that in complex notation are ż=(λ+i)z(zz̄)d−52(Az5+Bz4z̄+Cz3z̄2+Dz2z̄3+Ezz̄4+Fz̄5), where z=x+iy λ∈R and A,B,C,D,E,F∈C. Note that if d=5 we obtain the class of polynomial differential systems of the form 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. |
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