Physica D 200 (2005) 47–59 Renormalization for breakup of invariant tori

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. © 2004 Elsevier B.V. All rights reserved