19-45 Hans Koch

Golden mean renormalization for the almost Mathieu operator and related skew products (2944K, pdf) Jul 15, 19

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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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