ISSN:
1572-9478
Keywords:
chaos
;
KAM tori
;
cantori
;
asymptotic curves
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We find the form of cantori surrounding an island of stable motion in the standard map for various values of the nonlinearity parameter K near the value K = 5 (much larger than the critical value K cr = 0.971635...). The asymptotic curves of unstable periodic orbits inside the cantorus cross it after a certain time and then escape to the large chaotic sea. For K = 5 the crossing time (in appropriate units) is t = 1 and the escape time is t = 2. For 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,..] is 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 number is not the last KAM curve to be destroyed. Then we find that nearby orbits deviate considerably, but the average times spent near various resonance before escape are very similar.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1011197104118
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