The Number of Limit Cycles of a Polynomial System on the Plane

Abstract

We perturb the vector field $\dot{x}=-yC(x,y)$, $\dot{y}=xC(x,y)$ with a polynomial perturbation of degree $n$, where $C(x,y)=(\mathrm{1}-y^{\mathrm{2}}{)}^m$, and study the number of limit cycles bifurcating from the period annulus surrounding the origin.