Phase space of the standard map
The standard map (on the two-torus) is defined by
pn+1 = pn + k sin(pn+qn),
qn+1 = pn + qn.
This C-program
iterates one initial condition (p,q) a couple of times.
The plots below were generated by iterating about 100 random initial
conditions with this program.
For k=0.0 (above) the standard map reduces to rotations of the circle with
parameter p0.
For k=1.0 (above) we observe a mixture of (chains of) stable islands and
``chaotic'' regions.
For k=2.5 (above) a large part of phase space is occupied by a ``chaotic sea''
with only some stable islands remaining.
For k=7.0 (above) almost the whole phase space ``looks ergodic''. But when
magnifying, e.g., the region around (p,q)=(0.0,4.25) we can still find stable
islands (below).
Last modified: May 23 2001
Stefan Keppeler
(
stefan.keppeler@physik.uni-ulm.de)