Rapid Convergence to Frequency for Substitution Tilings of the Plane

Rapid Convergence to Frequency for Substitution Tilings of the Plane
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平面替换平铺的频率快速收敛

DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
J. Gambaudo
J. Gambaudo
中科院分区：
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文献类型：
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作者：
José Aliste;D. Coronel;J. Gambaudo

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本文研究欧几里得平面的自相似平铺。我们考虑给定瓷砖在以乔丹曲线为界的任何域中出现的次数。对于一大类自相似的平铺，包括许多众所周知的例子，我们给出了在其平均频率乘以区域内平铺总数周围出现次数的振荡的估计，其仅依赖于Jordan曲线。
This paper concerns self-similar tilings of the Euclidean plane. We consider the number of occurrences of a given tile in any domain bounded by a Jordan curve. For a large class of self-similar tilings, including many well-known examples, we give estimates of the oscillation of this number of occurrences around its average frequency times the total number of tiles in the domain, which depend only on the Jordan curve.