Abstract
The one-dimensional, discrete Schr\"odinger equation is studied when the potential is allowed to take on two values, ${V}_{A}$ and ${V}_{B}$, which are arranged according to a generalized Fibonacci sequence. The problem is reduced to a dynamical map for the traces of the transfer matrices which are given recursively by ${M}_{l+1}$=${M}_{l\mathrm{\ensuremath{-}}1}$${M}_{l}^{n}$, where n is a positive integer. A related class of sequences whose transfer matrices obey the recursion formula ${M}_{l+1}$=${M}_{l\mathrm{\ensuremath{-}}1}^{n}$${M}_{l}$ is also investigated.
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