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Journal Article

The Dynamical Properties of Penrose Tilings

E. Arthur Robinson, Jr.
Transactions of the American Mathematical Society
Vol. 348, No. 11 (Nov., 1996), pp. 4447-4464
https://www.jstor.org/stable/2155427
Page Count: 18
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The Dynamical Properties of Penrose Tilings
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Abstract

The set of Penrose tilings, when provided with a natural compact metric topology, becomes a strictly ergodic dynamical system under the action of R2 by translation. We show that this action is an almost 1:1 extension of a minimal R2 action by rotations on T4, i.e., it is an R2 generalization of a Sturmian dynamical system. We also show that the inflation mapping is an almost 1:1 extension of a hyperbolic automorphism on T4. The local topological structure of the set of Penrose tilings is described, and some generalizations are discussed.