Cool Chaos Demo: II.
Mixing in Chaotic Attractors.

Rössler's Funnel

One of Otto Rössler's enduring interests ⁽¹⁾  was the possibility of constructing a classification of chaotic motion. Such a taxonomy, he believed, should reflect the underlying geometry. According to this, the Rössler band exemplifies the simplest form of continuous chaos: motion on a Mobius strip with a single twist.⁽²⁾  Somewhat more complicated is motion on the so-called "Rössler funnel." Here, trajectiories can undergo an additional twist before being "plastered" back down on the central disk. The consequence is rapid mixing in both radial and azimuthal directions. (Click HERE to start.)

Notes and References

1. Rösser, O. E. 1979. Continuous chaos - four prototype equations. Pp. 376-392. In, Grure, O. and O. E. Rössler (eds.) Bifurcation Theory and Applications in Scientific Disciplines. N. Y. Acad. Sci. N. Y.

2. Abraham, R. H. and C. D. Shaw. 1982-1985. The Geometry of Behavior. Vol. 3. Aerial Press. Santa Cruz. Ca.