Dynamical systems with quasiperiodic behavior, ie, two incommensurate frequencies, may
be studied via discrete maps which show smooth continuous invariant curves with irrational
winding number. In this paper these curves are followed using renormalization group
techniques which are applied to a one-dimensional system (circle) and also to an area-
contracting map of an annulus. Two fixed points are found representing different types of
universal behavior: a trivial fixed point for smooth motion and a nontrivial fixed point. The …