2015
DOI: 10.1088/0951-7715/28/8/2617
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Distribution of patches in tilings and spectral properties of corresponding dynamical systems

Abstract: A tiling is a cover of R d by tiles such as polygons that overlap only on their borders. A patch is a configuration consisting of finitely many tiles that appears in tilings. From a tiling, we can construct a dynamical system which encodes the nature of the tiling. In the literature, properties of this dynamical system were investigated by studying how patches distribute in each tiling. In this article we conversely research distribution of patches from properties of the corresponding dynamical systems. We sho… Show more

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Cited by 1 publication
(3 citation statements)
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“…The goal of this article is to relate a interpretation of "order" with a dynamical property of objects such as tilings and Delone sets. This is an extension of [8].…”
Section: Introductionmentioning
confidence: 92%
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“…The goal of this article is to relate a interpretation of "order" with a dynamical property of objects such as tilings and Delone sets. This is an extension of [8].…”
Section: Introductionmentioning
confidence: 92%
“…Definition A.15. Let U be the set of all entourages generated by (8). The uniform structure defined by U is called the local matching uniform structure and the topology defined by it is called the local matching topology.…”
Section: Andmentioning
confidence: 99%
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