Elliptic limit cycles of two-dimensional autonomous differential systems
The authors consider the polynomial system \[ dx/dt = P(x,y),\quad dy/dt = Q(x,y),\tag{1} \] where the maximum \(n\) of the degrees of \(P,Q\) is at least 2, and study the problem of estimating the number of elliptic (or circular) limit cycles of (1). The main result is that there exist such systems (1) with \(n=4\) having 3 circular limit cycles with distinct centers lying on the same straight line. This shows a wrong assertion on circular limit cycles of (1) if \(n\) is even in the paper [\textit{N. Sadovskaia} and \textit{R. Ramires}, Tech. Report MA 2-IR-99-00015 (Version 2), Univ. Politech. de Cataluna (in Spanish)]
scientific article; zbMATH DE number 1916187