Spectral analysis of tridiagonal Fibonacci Hamiltonians
Spectral Theory
2013-04-11 v3 Mathematical Physics
Dynamical Systems
math.MP
Abstract
We consider a family of discrete Jacobi operators on the one-dimensional integer lattice, with the diagonal and the off-diagonal entries given by two sequences generated by the Fibonacci substitution on two letters. We show that the spectrum is a Cantor set of zero Lebesgue measure, and discuss its fractal structure and Hausdorff dimension. We also extend some known results on the diagonal and the off-diagonal Fibonacci Hamiltonians.
Keywords
Cite
@article{arxiv.1111.0953,
title = {Spectral analysis of tridiagonal Fibonacci Hamiltonians},
author = {W. N. Yessen},
journal= {arXiv preprint arXiv:1111.0953},
year = {2013}
}
Comments
28 pages, 55 references, 4 figures