The first reduction-of-dimension result (where a lower-dimensional dynamical system is shown to carry the qualitative properties of its higher-dimensional "parent") is due to Levinson. It is a perturbation theorem stating in effect that for sufficiently small periodic forcing of a planar autonomous system with a stable limit cycle the Poincare map possesses an attracting invariant circle. In other words, an exponentially stable invariant circle of a map persists under sufficiently small perturbations of the map.
Levinson's theorem is not specific as to the allowed size of perturbations but rather requires that these be sufficiently small. This limits the theorem's usefulness in applications. The theorem of this note asks more (the class of systems is more special, including forced pendula), but also gives more; the allowed size of perturbations is specified.
These results are then applied to determine parameter regions for which the resistively shunted Josephson junction is assuredly non-chaotic, no matter what forcing is applied. These results can account for the observed stability and voltage-to-frequency fidelity of the Kamper-Soulen resisteively shunted Josephson thermometer, in the region of low inductive shunting.