Previous renormalization analyses have demonstrated universal properties for the quasiperiodic transition to chaos. These theories have the unpleasant feature that universal properties depend on the winding number. We modify the renormalization transformation so that it has stable attractors. This allows us to study nonlocal properties by solving the equations numerically without linearizing. The resulting universal strange attractor contains the unstable fixed points of previous theories and has exponents that are independent of winding number.

• Received 26 November 1984

DOI:https://doi.org/10.1103/PhysRevA.31.3520