In this plot, the top 3 panels are the xy, yz, and xz projections of the orbit. The middle 3 panels show x, y and z as a funtion of time, and the bottom 3 panels show the power of the fft of x(t), y(t), and z(t). The top right tags are the number of the orbit, and whether it is chaotic (T) or not (F). We have constrained these orbits to the xy plane so we can directly compare the fft method to the surface of section method. (we have tested the transform technique on fully 3-d orbits, though). This means that the z plane should be always about zero. It is, although you can't tell that from the top row, because we allow SM to auto scale. In the bottom row, you can get a sense of the relative scale of the x, y, and z components, because we scaled the power in each panel to the maximum power of the 3 planes. Here's the orbit in the first time interval. If the .gif format is too sparse, try the postscript version.

And here is the orbit in the second time interval. Try the postscript plot if you can't see it well.

In this case, the power along the x-axes dramatically dampened by the second time interval, so much so that it is no longer the strongest principle frequency. It's tough to tell, by eye, whether this orbit is actually stochastic, although I have seen plots of stochastic tube orbits in which the stochasticity is very subtle. We are currently integrating this orbit for a much longer time interval, just to see how ergodic this orbit can become.