This Java Applet (JAVA version >= 1.4.2 required) displays the standard
nontwist map:
x(n+1) = x(n) + a { 1 - [y (n+1) ] ^2 }
y(n+1) = y(n) - b cos [ 2 pi x(n) ]
- The left half shows the phase space coordinates (x,y) of 700 iterations each for 20 different orbits. Click anywhere inside this plot to select new initial points/orbits. Symmetry lines and indicator points with their orbits are shown in gray.
- The right half shows the parameter space (a,b) region of interest. Click anywhere inside this graph to select a new parameter pair. Click on the legend on the top right to see examples on collision/reconnection/branching curves (text - odd orbit example, symbol - even orbit example) or to select the respective breakup parameter values.
- Anywhere below the jagged curve in parameter space, some
invariant orbits still exist, keeping all orbits from moving around too
freely in phase space. For parameters above the jagged curve, the
last invariant orbit is broken, and orbits can move freely between the top
and the bottom of phase space. If parameters on the jagged
parameter space curve are chosen (most easily by clicking on the
point markers in the legend
of the parameter space window), one sees the last invariant orbit (in
the center of phase space) turned fractal - a characteristic of being
right before its breakup.
- Watch your browser's status bar for the current map parameters and mouse coordinates.
- Click on any point outside the (a,b)-plot range to restore to the default initial values.
- Right-click on the Applet to toggle between color and black/white in the phase space view.
- Have fun! (And don't forget while playing that there is probably something much more important you should be doing right now...) ;)
For more detailed explanations, download my dissertation:
Gzipped PS (~4.6MB) -
PDF (~31MB)