STICKINESS AND CANTORI

We study the phenomenon of stickiness in the standard map. The sticky regions are limited by cantori. Most important among them are the cant ori with noble rotation numbers, that are approached by periodic orbit s corresponding to the successive truncations of the noble numbers. Th e size of an island of stability depends on the last KAM torus. As the perturbation increases, the size of the KAM curves increases. But the outer KAM curves are gradually destroyed and in general the island de creases. Higher-order noble tori inside the outermost KAM torus are al so destroyed and when the outermost KAM torus becomes a cantorus, the size of an island decreases abruptly. Then we study the crossing of th e cantori by asymptotic curves of periodic orbits just inside the cant orus. We give an exact numerical example of this crossing (non-schemat ic) and we find how the asymptotic curves, after staying for a long ti me near the cantorus, finally extend to large distances outwards. Fina lly, we End the relation between the forms of the sticky region and as ymptotic curves.