Recurrence of Kolmogorov-Arnold-Moser tori in nonanalytic twist maps

We study a class of twist maps where the functiong()=(1–|2|^z–1) is nonanalytic (C¹) and endowed with a varying degree of inflectionz. Whenz>3, reappearance of a KAM torus after its breakup has been observed. We introduce an inverse residue criterion to determine the reappearance point. Scaling behavior at the transition points is also studied. For 2z<3 the scaling exponents are found to vary withz, whereas forz3 they are independent ofz. In this sensez=3 plays a role quite similar to that of the upper critical dimension in phase transitions.