49 citations · 149 across the 13 of their papers we have counts for
4 papers · 1 filter
Asymptotic scaling and universality for skew products with factors in SL(2,R)
Hans Koch
We consider skew-product maps over circle rotations (mod 1) with factors that take values in SL(2,R). This includes maps of almost Mathieu type. In numerical experim…
On trigonometric skew-products over irrational circle-rotations
Hans Koch
We describe some asymptotic properties of trigonometric skew-product maps over irrational rotations of the circle. The limits are controlled using renormalization. The maps conside…
Renormalization and universality of the Hofstadter spectrum
Hans Koch, Sasha Kocic
We consider a renormalization transformation for skew-product maps of the type that arise in a spectral analysis of the Hofstadter Hamiltonian. Periodic orbits of determine…
Golden mean renormalization for the almost Mathieu operator and related skew products
Hans Koch
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…