## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Classification of centers, their cyclicity and isochronicity for a class of polynomial differential systems of degree $d\geq 7$ odd

#### Abstract

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 $A,B,C,D \in \mathbb{C}$.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 17, Number 5 (2010), 859-873.

Dates
First available in Project Euclid: 14 December 2010

https://projecteuclid.org/euclid.bbms/1292334061

Digital Object Identifier
doi:10.36045/bbms/1292334061

Mathematical Reviews number (MathSciNet)
MR2777776

Zentralblatt MATH identifier
1230.37027

#### Citation

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 17 (2010), no. 5, 859--873. doi:10.36045/bbms/1292334061. https://projecteuclid.org/euclid.bbms/1292334061