Golden mean renormalization for the almost Mathieu operator and related skew products
نویسندگان
چکیده
Considering SL(2,R) skew-product maps over circle rotations, we prove that a renormalization transformation associated with the golden mean α* has nontrivial periodic orbit of length 3. We also present some numerical results, including evidence this period 3 describes scaling properties Hofstadter butterfly near top spectrum at and generalized eigenfunction for energy.
منابع مشابه
The Spectrum of the Almost Mathieu Operator
The notes are based on a series of six lectures, given during my stay at the CRC 701 in June/July 2008. The lecture series intended to give a survey of some of the results for the almost Mathieu operator that have been obtained since the early 1980’s. Specifically, the metalinsulator transition is discussed in detail, along with its relation to the ten Martini problem via duality and reducibility.
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2021
ISSN: ['0022-2488', '1527-2427', '1089-7658']
DOI: https://doi.org/10.1063/5.0005429