Spectral analysis of tridiagonal Fibonacci Hamiltonians

Details Spectral analysis of tridiagonal Fibonacci Hamiltonians Spectral analysis of tridiagonal Fibonacci Hamiltonians

2011-11-03

arxiv.org/abs/1111.0953v3

Mathematics

Spectral Theory

28 pages, 55 references, 4 figures

Scientific paper

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.

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