Title: Golden mean renormalization for the almost Mathieu operator and related skew products
Author: H. Koch
Abstract:   Considering SL(2,R) skew-product maps over circle rotations, we prove that a renormalization transformation associated with the golden mean α* has a nontrivial periodic orbit of length 3. We also present some numerical results, including evidence that this period 3 describes scaling properties of the Hofstadter butterfly near the top of the spectrum at α* and scaling properties of the generalized eigenfunction for this energy.
Paper: Preprint (old version) and programs