The dynamical properties of Penrose tilings
Author: E. Arthur Robinson Jr.
Journal: Trans. Amer. Math. Soc. 348 (1996), 4447-4464
MSC (1991): Primary 28D05; Secondary 28D20
MathSciNet review: 1355301
Abstract: The set of Penrose tilings, when provided with a natural compact metric topology, becomes a strictly ergodic dynamical system under the action of by translation. We show that this action is an almost 1:1 extension of a minimal action by rotations on , i.e., it is an generalization of a Sturmian dynamical system. We also show that the inflation mapping is an almost 1:1 extension of a hyperbolic automorphism on . The local topological structure of the set of Penrose tilings is described, and some generalizations are discussed.
E. Arthur Robinson Jr.
Affiliation: Department of Mathematics, The George Washington University, Washington, D.C. 20052
Keywords: Tilings, topological dynamics, almost periodicity
Received by editor(s): May 13, 1995
Additional Notes: Partially supported by a George Washington University Committee on Research UFF grant and by NSF grant DMS-9303498
Article copyright: © Copyright 1996 American Mathematical Society