Hamiltonian Chaos - Demo 2

2D Circle Map: .... and Area Preserving.

Now look at the same parameters except b=1. For each demonstration click on various points of the running plot to start from new initial conditions.

You should find a rich variety of behavior for each set of parameters with

• Tori (appearing as curves traversing the plot) that are remnants of the tori of the integrable system a=0. These curves have irrational winding number, i.e. quasiperiodic motion.
• "Island chains" of elliptical orbits (tori) surrounding discrete points giving finite winding number corresponding to frequency locked orbits.
• Chaotic orbits that are most easily found in the hyperbolic regions between two elliptical islands.