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Centers for a class of generalized quintic polynomial differential systems

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Issue date
2014
Author
Giné, Jaume
Llibre, Jaume
Valls, Claudia
Suggested citation
Giné, Jaume; Llibre, Jaume; Valls, Claudia; . (2014) . Centers for a class of generalized quintic polynomial differential systems. Applied Mathematics and Computation, 2014, vol. 242, p. 187-195. https://doi.org/10.1016/j.amc.2014.05.047.
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Abstract
We classify the centers of the polynomial differential systems in R2 of degree d ≥ 5 odd that in complex notation writes as z˙ = iz + (zz¯)d−5/2 (Az5 + Bz4z¯ + Cz3z¯2 + Dz2z¯3 + Ezz¯4 + Fz¯5), where A, B, C, D, E, F ∈ C and either A = Re(D) = 0, or A = Im(D) = 0, or Re(A) = D = 0, or Im(A) = D = 0.
URI
http://hdl.handle.net/10459.1/60383
DOI
https://doi.org/10.1016/j.amc.2014.05.047
Is part of
Applied Mathematics and Computation, 2014, vol. 242, p. 187-195
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  • Centers for generalized quintic polynomial differential systems 

    Giné, Jaume; Llibre, Jaume; Valls, Claudia (Rocky Mountain Mathematics Consortium, 2017)
    We classify the centers of polynomial differential systems in $R^2$ of odd degree $d \ge 5$, in complex notation, as $\dot{z} = iz + (z \bar z)^(d-5)/2(A z^5 + B z^4 \bar z + C z^3 \bar z^2 + D z^2 \bar z^3 + E z \bar z^4 ...
  • Centers and isochronous centers for generalized quintic systems 

    Giné, Jaume; Llibre, Jaume; Valls, Claudia (Elsevier, 2015)
    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), ...
  • The Hopf cyclicity of the centers of a class of quintic polynomial vector fields 

    García, I. A. (Isaac A.); Llibre, Jaume; Maza Sabido, Susanna (Elsevier, 2015-01-20)
    We consider families of planar polynomial vector fields having a singularity with purely imaginary eigenvalues for which a basis of its Bautin ideal B is known. We provide an algorithm for computing an upper bound of the ...

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