We consider a family of discrete Jacobi operators on the one-dimensional
integer lattice with Laplacian and potential terms modulated by a primitive
invertible two-letter substitution. We investigate the spectrum and the
spectral type, the fractal structure and fractal dimensions of the spectrum,
exact dimensionality of the integrated density of states, and the gap
structure. We present a review of previous results, some applications, and open
problems. Our investigation is based largely on the dynamics of trace maps.
This work is an extension of similar results on Schroedinger operators,
although some of the results that we obtain differ qualitatively and
quantitatively from those for the Schoedinger operators. The nontrivialities of
this extension lie in the dynamics of the associated trace map as one attempts
to extend the trace map formalism from the Schroedinger cocycle to the Jacobi
one. In fact, the Jacobi operators considered here are, in a sense, a test
item, as many other models can be attacked via the same techniques, and we
present an extensive discussion on this.Comment: 41 pages, 5 figures, 81 reference
