EXAMPLES OF CENTER CYCLICITY BOUNDS USING THE REDUCED BAUTIN DEPTH

There is a method for bounding the cyclicity of non-degenerate monodromic singularities of polynomial planar families of vector fields X-lambda. which can work even in the case that the Poincare first return map has associated a non-radical Bautin ideal B. The method is based on the stabilization of the integral closures of an ascending chain of polynomial ideals in the ring of polynomials in the parameters lambda of the family that stabilizes at B. In this work we use computational algebra methods to provide an explicit example in which the classical procedure to find the Bautin depth of B fails but the new approach is successful.