Higher order limit cycle bifurcations from non-degenerate centers

Abstract

The computational problems which appear in the computation of the Poincaré–Liapunov constants and the determination of their functionally independent number has led in recent works to consider only the lowest terms of these constants. In this work we improve the results obtained in this direction for polynomials systems of the form x˙=-y+Pn(x,y),y˙=x+Qn(x,y), where Pn and Qn are a homogeneous polynomial of degree n. We use center bifurcation to estimate the cyclicity of a unique singular point of focus-center type for different values of n and compare with the results given by the conjecture presented in [15].