Abstract
In this paper, we use renormalization methods to study self-similarity in the fluctuations ηi of the Harper equation in the strong-coupling limit for quadratic irrationals of the form (a2+4−a)/2 for a∈N. Using the decimation method, we obtain a second-order functional recurrence which we prove rigorously has an entire fixed point. This fixed point governs the scaling of the fluctuations ηi in the strong-coupling limit.
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