Lyapunov Exponents - Demo 3

2D Circle Map

The 2D circle map will be studied in detail in chapter 18. Here we just notice that for quasiperiodic motion, one of the Lyapunov exponents is zero (corresponding to a perturbation along the orbit) and one negative (corresponding to collapse onto the orbit):

whereas for values giving chaotic motion, the largest exponent is positive:

You can convince yourself that the motion is chaotic by enlarging portions of the map near the "crinkles" to observe the fractal structure.

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Last modified Tuesday, December 7, 1999
Michael Cross