Trace maps
Trace maps are dynamical systems derived from the action of substitution
rules on matrix products of which traces are calculated. They are relevant
in renormalization schemes for the one-dimensional quasiperiodic Schrodinger
equation (where there is a relationship between the nonwandering sets of
trace maps and its spectrum) and also for transport properties (eg diffraction)
through stacked monolayers.
The research focusses on several issues:
- Dynamics of trace maps for 2x2 matrices with invertible substitution
rules. The dynamics of these trace maps is estetically very appealing.
Despite that they have been around since the early 1980s, the main
questions (eg hyperbolicity) are still largely open.
- Trace maps for nxn matrices, possibly with structures. Important questions
involve the nr of variables needed and the influence of (physically
motivated) structures.
Work in progress with Stephen Bedding (La Trobe Melbourne).