- 92-135 Radin C.
- SPACE TILINGS AND SUBSTITUTIONS
Oct 12, 92
(auto. generated ps),
of related papers
Abstract. We generalize the study of symbolic dynamical systems of finite type
and $\Z^2$ action, and the associated use of symbolic substitution
dynamical systems, to dynamical systems with $\R^2$ action. The new
systems are associated with tilings of the plane.
We generalize the classical technique of the matrix of a substitution
to include the geometrical information needed to study tilings, and we
utilize rotation invariance to eliminate discrete spectrum. As an example
we prove that Conway's pinwheel tilings have no discrete spectrum.