Previous renormalisation analyses have demonstrated universal properties for the quasi periodic transition to chaos. These theories have the unpleasant feather there universal properties depend on the winding number. We modify the renormalisation transformation so that is has stable attractors. This allows us to study nonlocal properties by solving the equations numerically without linearising. The resulting universal strange attractor contains the unstable fixed points of previous theories and has exponents that are independent of winding number.
Farmer, J.D. & Satija, I.I. (1985). 'Renormalization of the Quasiperiodic Transition to Chaos for Arbitrary Winding Numbers'. Physical Review A, 31(5), pp.3520-3522.