It is shown numerically that the stability intervals for limit cycles of the circle map form a complete devil's staircase at the onset of chaos. The complementary set to the stability intervals is a Cantor set of fractal dimension $D=0.87\mathrm{}$. This exponent is found to be universal for a large class of functions.

• Received 18 March 1983

DOI:https://doi.org/10.1103/PhysRevLett.50.1637