BRANCHING-RULES AND GAP-LABELING PROPERTIES FOR A CLASS OF ONE-DIMENSIONAL QUASI-LATTICES

The gap-labeling properties of the energy spectrum for a class of one- dimensional quasilattices have been investigated. We have studied the branching rules on subbands of the hierarchical energy spectrum and ob tained the integrated density of states (IDOS). It is analytically pro ved that IDOS has the form n + ma, where n and m are integers, alpha = root 2 - 1. The characteristic number m can be used to label the corr esponding energy gap. conclusion is similar to that of one-dimensional Fibonacci quasicrystals.