Golden mean renormalization for the almost Mathieu operator and related skew products
Mathematical Physics
2024-06-19 v2 math.MP
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.
Keywords
Cite
@article{arxiv.1907.06804,
title = {Golden mean renormalization for the almost Mathieu operator and related skew products},
author = {Hans Koch},
journal= {arXiv preprint arXiv:1907.06804},
year = {2024}
}
Comments
The source code for our programs, as well as data files, can be found at http://web.ma.utexas.edu/users/koch/papers/skewrg/