Some novel critical phenomena are discovered in a class of nonanalytic twist maps. It is found that the degree of inflection z plays a role reminiscent of that of dimensionality in phase transitions with z=2 and 3 corresponding to the lower and upper critical dimensions, respectively. Moreover, recurrence of invariant circles has also been observed. An ‘‘inverse residue criterion,’’ complementary to the ‘‘residue criterion’’ for the determination of the disappearance point, is introduced to determine the reappearance point of invariant circles.

• Received 8 October 1990

DOI:https://doi.org/10.1103/PhysRevA.43.4249