Classification of the centers, of their cyclicity and isochronicity for two classes of generalized quintic polynomial differential systems
This article deals with the center-focus problem for a class of polynomial differential systems in \({\mathbb{R}^2}\) of degree \(d\) that in complex notation \(z = x + iy\) can be written as \[ \dot z = (\lambda+i) z + (z \overline{z})^{\frac{d-5}{2}} \left(A z^{4+j} \overline{z}^{1-j} + B z^3 \overline{z}^2 + C z^{2-j} \overline{z}^{3+j}+D \overline{z}^5\right), \] where \(j\) is either 0 or 1, \(d\) is an arbitrary odd positive integer greater than or equal to five, \({\lambda \in \mathbb{R}}\), and \({A,B,C,D \in \mathbb{C}}\). The authors are mainly interested in finding new families of centers of such a systems as well as in studying their cyclicity and isochronicity.
scientific article; zbMATH DE number 5636894