Classification of centers, their cyclicity and isochronicity for a class of polynomial differential systems of degree $d\geq 7$ odd
Llibre, Jaume ; Valls, Clàudia
Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, p. 859-873 / Harvested from Project Euclid
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In this paper we classify the centers, the cyclicity of its Hopf bifurcation and the isochronicity of the polynomial differential systems in $\mathbb{R}^2$ of degree $d\geq 7$ odd that in complex notation $z=x+ i y$ can be written as \[ \dot z = (\lambda+i) z + (z \overline z)^{\frac{d-7}2} (A z^6 \overline z + B z^4 \overline z^3 + C z^2 \overline z^5 +D \overline z^7), \] where $\lambda \in \mathbb{R}$, and $A,B,C,D \in \mathbb{C}$.
Publié le : 2010-12-15
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@article{1292334061,
     author = {Llibre, Jaume and Valls, Cl\`audia},
     title = {Classification of centers, their cyclicity and isochronicity for a class of
polynomial differential systems of degree $d\geq 7$ odd},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {17},
     number = {1},
     year = {2010},
     pages = { 859-873},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1292334061}
}

Llibre, Jaume; Valls, Clàudia. Classification of centers, their cyclicity and isochronicity for a class of
polynomial differential systems of degree $d\geq 7$ odd. Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, pp.  859-873. http://gdmltest.u-ga.fr/item/1292334061/