“…In fact, finite cyclicity of any limit periodic set, in terms of the degree of the system, implies the solution to Hilbert's 16th problem. The cyclicity problem has been studied by several authors also in its relation with the center problem, see for instance [4,5,7,10,11,12,18]. Roughly speaking, the cyclicity of a limit periodic set of a polynomial system of degree at most d, is the maximum number of limit cycles that can bifurcate from the given limit periodic set inside the family of all polynomial systems of degree d; see Definition 12 in [25] for a precise definition.…”