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

Abstract

We consider the spectrum of discrete Schrödinger 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.

arXiv comment12 pages, to appear in Commun. Math. Phys

References in corpus (5)

• Uniform spectral properties of one-dimensional quasicrystals, III. $\alpha$-continuity
• The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian
• Spectra of Discrete Schrödinger Operators with Primitive Invertible Substitution Potentials
• The fractal dimensions of the spectrum of Sturm Hamiltonian
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Cited by in corpus (1)

• The spectral characteristics of the Sturm Hamiltonian with eventually periodic type