The dynamical properties of Penrose tilings
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- by E. Arthur Robinson Jr. PDF
- Trans. Amer. Math. Soc. 348 (1996), 4447-4464 Request permission
Abstract:
The set of Penrose tilings, when provided with a natural compact metric topology, becomes a strictly ergodic dynamical system under the action of $\mathbf {R}^2$ by translation. We show that this action is an almost 1:1 extension of a minimal $\mathbf {R}^2$ action by rotations on $\mathbf {T}^4$, i.e., it is an $\mathbf {R}^2$ generalization of a Sturmian dynamical system. We also show that the inflation mapping is an almost 1:1 extension of a hyperbolic automorphism on $\mathbf {T}^4$. The local topological structure of the set of Penrose tilings is described, and some generalizations are discussed.References
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Additional Information
- E. Arthur Robinson Jr.
- Affiliation: Department of Mathematics, The George Washington University, Washington, D.C. 20052
- Email: robinson@math.gwu.edu
- 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
- © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 348 (1996), 4447-4464
- MSC (1991): Primary 28D05; Secondary 28D20
- DOI: https://doi.org/10.1090/S0002-9947-96-01640-6
- MathSciNet review: 1355301