This is a tour
through 16 successive Poincaré sections
of the flow of a chaotic
vertically driven pendulum with
friction. One of the hallmarks of chaos is stretching and folding
of the manifold on which the dynamics take place. The stretching
and folding can be easily seen as we move our attention through successive
values of the drive phase.
This wire frame torus contains a stable period six orbit of the pendulum. At these parameter values,
a stable period two also exists. For different initial conditions, either stable state may be obtained.
