92-135 Radin C.

SPACE TILINGS AND SUBSTITUTIONS (130K, postscript) Oct 12, 92

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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.

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