POLYNOMIAL SYSTEMS - A LOWER-BOUND FOR THE HILBERT-NUMBERS

Let H-n be the maximum possible number of limit cycles of systems x= P(x, y), y = Q(x, y), where P and Q are polynomials of degree at most n. We are concerned with the rate of growth of H-n as n increases: it is known that H-n greater than or equal to kn(2) for some constant k. In this paper we show that H-n grows at least as rapidly as n(2) log n.