Hans Koch
Golden mean renormalization 
for the almost Mathieu operator and related skew products
(2944K, pdf)

ABSTRACT.  Considering SL(2,R) skew-product maps 
over circle rotations, we prove that 
a renormalization transformation associated with the golden mean alpha 
has a nontrivial periodic orbit of length 3. 
We also present some numerical results, 
including evidence this period 3 describes 
scaling properties of the Hofstadter butterfly 
near the top of the spectrum at alpha, 
and scaling properties of the generalized eigenfunction for this energy.