CRM CAMP in Nonlinear Analysis

Computer-Assisted Mathematical Proofs in Nonlinear Analysis

February 2, 2021 from 10:00 to 11:00 (Montreal/EST time) Zoom meeting

Golden mean renormalization for the almost Mathieu operator and related skew products

Seminar presented by Hans Koch (University of Texas at Austin, USA)

We renormalize SL(2,R) skew-product maps over circle rotations. Such maps arise e.g. in the spectral analysis of the Hofstadter Hamiltonian and the almost Mathieu operator. For rotations by the inverse golden mean, we prove the existence of two renormalization-periodic orbits. We conjecture that there are infinitely many such orbits, and that the associated universal constants describe local scaling properties of the Hofstadter spectrum and of the corresponding generalized eigenvectors. Some recent results on trigonometric skew-product maps will be described as well. This is joint work with Saša Kocić (UT Austin, USA).