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

Abstract: 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).

analysis of PDEsclassical analysis and ODEsdynamical systemsfunctional analysisnumerical analysis

Audience: researchers in the discipline

CRM CAMP (Computer-Assisted Mathematical Proofs) in Nonlinear Analysis

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