Double devil's staircase in circle maps.

Abstract

Motivated by the existence of a fractal phase boundary for the occurrence of Kolmogorov-Arnold-Moser tori in two-parameter area-preserving maps, we study the two-parameter circle map with two inflection points. The critical surface of the mode-locked windows is found to obey additive rules for the bistability regimes caused by cusp catastrophe. This results in the double devil's staircase for the mode-locked windows and a fractal curve for a critical set of parameter values for the breakup of the invariant circles.