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

초록

We study a class of twist maps where the function g(θ)=θ(1-|2 θ|z-1) is nonanalytic (C1) and endowed with a varying degree of inflection z. When z>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 2≤z<3 the scaling exponents are found to vary with z, whereas for z≥3 they are independent of z. In this sense z=3 plays a role quite similar to that of the upper critical dimension in phase transitions. © 1991 Plenum Publishing Corporation.

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