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.

12 pages, to appear in Commun. Math. Phys

Cited by in corpus (1)

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