Algebraic Limit Cycles Bifurcating from Algebraic Ovals of Quadratic Centers

Abstract

In the integrability of polynomial differential systems it is well known that the invariant algebraic curves play a relevant role. Here we will see that they can also play an important role with respect to limit cycles.In this paper, we study quadratic polynomial systems with an algebraic periodic orbit of degree [Formula: see text] surrounding a center. We show that there exists only one family of such systems satisfying that an algebraic limit cycle of degree [Formula: see text] can bifurcate from the period annulus of the mentioned center under quadratic perturbations.