CYCLICITY OF A CLASS OF POLYNOMIAL NILPOTENT CENTER SINGULARITIES

In this work we extend techniques based on computational algebra for bounding the cyclicity of nondegenerate centers to nilpotent centers in a natural class of polynomial systems, those of the form (x) over dot = y + P-2m vertical bar 1(x, y), (y) over dot = Q(2m+1)(x, y), where P2m+1 and Q(2m+1) are homogeneous polynomials of degree 2m+1 in x and y. We use the method to obtain an upper bound (which is sharp in this case) on the cyclicity of all centers in the cubic family and all centers in a broad subclass in the quintic family.