A.Apte, A.Wurm, P.J.Morrison
Renormalization for breakup of invariant tori
(390K, RevTeX 4)

ABSTRACT.  We present renormalization group operators for the breakup of 
invariant tori with winding numbers that are quadratic irrationals. 
We find the simple fixed points of these operators and interpret the 
map pairs with critical invariant tori as critical fixed points. 
Coordinate transformations on the space of maps relate these fixed 
points, and also induce conjugacies between the corresponding 
operators.