This code simulates that breaking of KAM Tori in a nearly
integrable system. It allows you to see how different integration methods
effect the results. It was written by
Mark Lewis.
The display shows a Poincare section for a simple non-physical system in
action angle variables. The Hamiltonian of the system has the form H=H_0+eH_1
where H_0 is integrable and H_1 isn't. The e is the epsilon value that can be
input in the applet. For a value of zero a number of points or a circle will
be drawn. These circles break down as epsilon is increased to become space
filling. For some reason the structures created by this applet are not
exactly what one is used to seeing when dealing with KAM Tori and homoclinic
tangles, but the point is still reasonably well illustrated.
With small values of epsilon, using the symplectic maps, it is possible to
increas the time step to the point where tori that should be preserved break
down.
To change the value of alpha, the ratio of the frequencies of the two positions
of the system, simply click the mouse at different distances from the center
of the image.
The source.