Localization of Invariant Spanning Curves

We discuss in this chapter a procedure using a connection with the standard map to determine the localization of the first invariant spanning curve above of the chaotic sea. The idea is to use a transition from local to global chaos observed in the standard mapping to describe the position of the first invariant spanning curve in a family of mappings which the angles diverge in the limit of vanishingly action. The knowledge of the first invariant spanning curve is useful in the characterization of the scaling discussed in the forthcoming chapter.