TRACE MAPS

Trace maps for products of transfer matrices prove to be an important tool in the investigation of electronic spectra and wave functions of one-dimensional quasiperiodic systems. These systems belong to a gener al class of substitution sequences. In this work we review the various stages of development in constructing trace maps for products of (2 x 2) matrices generated by arbitrary substitution sequences. The dimens ion of the underlying space of the trace map obtained by means of this construction is the minimal possible, namely 3r - 3 for an alphabet o f size r greater than or equal to 2. In conclusion, we describe some r esults from the spectral theory of discrete Schrodinger operators with substitution potentials.