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arXiv · 1907.06804

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

Hans Koch
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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.

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Hans Koch. 2019-07-16. Golden mean renormalization for the almost Mathieu operator and related skew products. https://doi.org/10.1063/5.0005429

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