Trace Maps
1997 ◽
Vol 11
(30)
◽
pp. 3525-3542
◽
Keyword(s):
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 general class of substitution sequences. In this work we review the various stages of development in constructing trace maps for products of (2×2) matrices generated by arbitrary substitution sequences. The dimension of the underlying space of the trace map obtained by means of this construction is the minimal possible, namely 3r-3 for an alphabet of size r≥2. In conclusion, we describe some results from the spectral theory of discrete Schrödinger operators with substitution potentials.
1992 ◽
Vol 06
(03n04)
◽
pp. 281-320
◽
1991 ◽
Vol 52
(7)
◽
pp. 835-839
◽
2012 ◽
Vol 400
(3)
◽
pp. 032065
Keyword(s):