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- W2073058369 abstract "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." @default.
- W2073058369 created "2016-06-24" @default.
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- W2073058369 date "2010-01-30" @default.
- W2073058369 modified "2023-09-26" @default.
- W2073058369 title "Pisot family self-affine tilings, discrete spectrum, and the Meyer property" @default.
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