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3rd Austrian Hungarian Workshop
Barbara Funk
Florian Freistetter
Rudolf Dvorak
The Universality of Escape in the Standardmap
We checked the behaviour of the standard-map for large nonlinearity parameters (up to K = 130) : it
turned out that with a period of pi there appear islands on the edge, respectively in the middle of the plane.
They have a selfsimilar structure and seem to diminish in size exponentally. But also in between these values of K, where
larger islands are present, we observe tiny islands -- which are possibly present for ALL values of K. The results are
confirmed using three different methods: a counting of pointless boxes, a counting of points in every box (1000 by 1000)
for very large iterations (up to 10E9) and also a counting of boxes which are penetrated by a single orbit (also up to
10E9) iterations. |