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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