# 2D Circle Map - Demo 3

## Breakdown of the torus

Now increase *a* to *1.2*:

The smooth curve has "crinkled". Enlarging various regions of the plot (outline an interesting region with with the mouse on a stopped plot), e.g. the fold around x=0.8, shows a multi-layered structure, so that the curve no longer has the topology of a circle. The torus corresponding to quasiperiodic motion has broken down, and the dynamics is now chaotic. The largest Lyapunov exponent is now positive.

[Previous Demonstration]
[Next Demonstration]
[Introduction]

Last modified Tuesday, December 14, 1999

Michael Cross