The Dynamical Properties of Penrose Tilings
نویسنده
چکیده
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.
منابع مشابه
AN ALGEBRAIC INVARIANT FOR SUBSTITUTION TILING SYSTEMSbyCharles Radin
We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We deene an isomorphism invariant related to a subgroup of rotations and compute it for various examples. We also extend our analysis to more general dynamical systems.
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We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We define an isomorphism invariant related to a subgroup of rotations and compute it for various examples. We also extend our analysis to more general dynamical systems.
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We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We deene an isomorphism invariant related to a subgroup of rotations and compute it for various examples. We also extend our analysis to more general dynamical systems.
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