Almost Sure Frequency Independence of the Dimension of the Spectrum of Sturmian Hamiltonians

Anton Gorodetski (UC Irvine); David Damanik (Rice University)

arxiv: 1406.4810 · v2 · pith:CK3T7IBVnew · submitted 2014-06-18 · 🧮 math.SP · math-ph· math.DS· math.MP

Almost Sure Frequency Independence of the Dimension of the Spectrum of Sturmian Hamiltonians

David Damanik (Rice University) , Anton Gorodetski (UC Irvine) This is my paper

classification 🧮 math.SP math-phmath.DSmath.MP

keywords dimensionalmostfrequencyspectrumsturmianconsidercountingcoupling

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We consider the spectrum of discrete Schr\"odinger operators with Sturmian potentials and show that for sufficiently large coupling, its Hausdorff dimension and its upper box counting dimension are the same for Lebesgue almost every value of the frequency.

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Almost Sure Frequency Independence of the Dimension of the Spectrum of Sturmian Hamiltonians

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