Centers and isochronous centers for generalized quintic systems

Jaume Giné, Jaume Llibre, Claudia Valls

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3 Citations (Scopus)


© 2014 Elsevier B.V. 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+(zz¯)d-52(Az5+Bz4z¯+Cz3z¯2+Dz2z¯3+Ezz¯4+Fz¯5), where z=x+iy, λ&rdblR and A,B,C,D,E,F&Cdbl 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.
Original languageEnglish
Pages (from-to)173-186
JournalJournal of Computational and Applied Mathematics
Publication statusPublished - 1 May 2015


  • Computation on modular arithmetics
  • Gröbner basis theory
  • Non-degenerate center
  • PoincaréLiapunovAbel constants


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