Pisot family self-affine tilings, discrete spectrum, and the Meyer property
Pisot family self-affine tilings, discrete spectrum, and the Meyer property
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Pisot 族自仿射平铺、离散谱和 Meyer 性质
DOI：
10.3934/dcds.2012.32.935
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发表时间：
2010
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通讯作者：
B. Solomyak
中科院分区：
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作者：
Jeong;B. Solomyak
We consider self-affine tilings in the Euclidean space and the associated tiling dynamical systems, namely, the translation action on the orbit closure of the given tiling. We investigate the spectral properties of the system. It turns out that the presence of the discrete component depends on the algebraic properties of the eigenvalues of the expansion matrix $\phi$ for the tiling. Assuming that $\phi$ is diagonalizable over $\C$ and all its eigenvalues are algebraic conjugates of the same multiplicity, we show that the dynamical system has a relatively dense discrete spectrum if and only if it is not weakly mixing, and if and only if the spectrum of $\phi$ is a "Pisot family". Moreover, this is equivalent to the Meyer property of the associated discrete set of "control points" for the tiling.
Shunsuke Morosawa：“关于残差 Julia 集的理性函数”Ergod & Dynam。
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复杂的皮索计数系统和自相似平铺
DOI：
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发表时间：
2007
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作者：
古門麻貴;伊藤俊次;伊藤俊次;伊藤俊次;伊藤俊次;伊藤俊次;伊藤俊次;伊藤俊次;伊藤俊次;伊藤俊次;伊藤俊次
通讯作者：
伊藤俊次