English

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