The Spectrum and the Spectral Type of the Off-Diagonal Fibonacci Operator
Spectral Theory
2008-07-25 v2 Dynamical Systems
Abstract
We consider Jacobi matrices with zero diagonal and off-diagonals given by elements of the hull of the Fibonacci sequence and show that the spectrum has zero Lebesgue measure and all spectral measures are purely singular continuous. In addition, if the two hopping parameters are distinct but sufficiently close to each other, we show that the spectrum is a dynamically defined Cantor set, which has a variety of consequences for its local and global fractal dimension.
Keywords
Cite
@article{arxiv.0807.3024,
title = {The Spectrum and the Spectral Type of the Off-Diagonal Fibonacci Operator},
author = {David Damanik and Anton Gorodetski},
journal= {arXiv preprint arXiv:0807.3024},
year = {2008}
}
Comments
10 pages; corrected a few typos