Self-Similar Tiling Systems, Topological Factors and Stretching Factors
نویسندگان
چکیده
منابع مشابه
Self-Similar Tiling Systems, Topological Factors and Stretching Factors
In this paper we prove that if two self-similar tiling systems, with respective stretching factors λ1 and λ2, have a common factor which is a non periodic tiling system, then λ1 and λ2 are multiplicatively dependent.
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The purpose of this paper is to give the flavor of the subject of self-similar tilings in a relatively elementary setting, and to provide a novel method for the construction of such polygonal tilings.
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We consider infinite measure-preserving non-primitive selfsimilar tiling systems in Euclidean space R. We establish the secondorder ergodic theorem for such systems. The speed of convergence is determined by the Hausdorff dimension of a graph-directed set associated to the substitution rule.
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15 صفحه اولA self-similar tiling generated by the minimal Pisot number
Let be a Pisot unit of degree 3 with a certain niteness condition. A large family of self similar plane tilings can be constructed, by the digit expansion in base . (cf. [7], [5], [8]) In this paper, we prove that the origin is an inner point of the central tile K. Further, in the case corresponds to the minimal Pisot number, we shall give a detailed study on the fractal boundary of each tile. ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2008
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-008-9108-4