The number of limit cycles of a polynomial system on the plane (Q2015582)

The paper is devoted to a perturbed planar system of the form \[ \dot{x}=-yC(x,y) +\varepsilon P(x,y), \quad \dot{y}=xC(x,y)+\varepsilon Q(x,y), \] where \(\varepsilon \) is a small real parameter, \(C(x,y)=(1-y^2)^m\) and \(P(x,y), Q(x,y)\) are real polynomials of degree \(n\). By studying the number of zeros of the corresponding abelian integral the authors estimate the number of limit cycles bifurcating from the period annulus surrounding the origin of the unperturbed planar system.