Bifurcation of Limit Cycles from a Quasi-Homogeneous Degenerate Center

Abstract

In this paper, we deal with the following differential system [Formula: see text] where p, q are positive integers, and P(x, y), Q(x, y) are real polynomials of degree n, we obtain an upper bound for the maximum number of limit cycles bifurcating from the period annulus of a quasi-homogeneous center, that is (n - 1)p1 + (t + 1)q - 1 + 2rp1q1(q + 3) + 2tqrp1q1, where t = [n/2q] + 2, (p, q) = r(p1, q1), p1 and q1 are coprime.