, Volume 254, Issue 2, pp 343-359
Date: 05 Nov 2004

Conjugacies for Tiling Dynamical Systems

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Abstract

We consider tiling dynamical systems and topological conjugacies between them. We prove that the criterion of being of finite type is invariant under topological conjugacy. For substitution tiling systems under rather general conditions, including the Penrose and pinwheel systems, we show that substitutions are invertible and that conjugacies are generalized sliding block codes.

Communicated by G. Gallavotti
Research supported in part by NSF Vigre Grant DMS-0091946
Research supported in part by NSF Grant DMS-0071643 and Texas ARP Grant 003658-158
Acknowledgement The authors are grateful for the support of the Banff International Research Station, at which we formulated and proved Theorem 3.