Crossing of various cantori

We find the form of cantori surrounding an island of stable motion in the s tandard map for various values of the nonlinearity parameter K near the val ue K = 5 (much larger than the critical value K-cr = 0.971635...). The asym ptotic curves of unstable periodic orbits inside the cantorus cross it afte r a certain time and then escape to the large chaotic sea. For K = 5 the cr ossing time (in appropriate units) is t = 1 and the escape time is t = 2. F or K = 4.998 the crossing time is t = 7 and the escape time t = 23000. This delay of escape is due to the existence of higher order cantori, with very small gaps. We found that, as K increases the noble torus [2,4, 1, 1,..] i s destroyed before the destruction of the higher order tori [2,4,1,1,1,1,2, 1....] and [2,4,1,1,1,1,3,1,..]. Thus the torus with the simplest noble num ber is not the last KAM curve to be destroyed. Then we find that nearby orb its deviate considerably, but the average times spent near various resonanc e before escape are very similar.