Abstract
We consider one-dimensional quasiperiodic Fibonacci tilings. Namely, we study sets of vertices of these tilings that represent one-dimensional quasilattices defined on the base of a parameterization by rotations of a circle, and the distribution of points of quasilattices with respect to a variable module. We show that the distribution with respect to some modules is not uniform. We describe the distribution function and its integral representation, and estimate the remainder in the problem of the distribution of points of a quasilattice for corresponding modules.
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Original Russian Text © V.V. Krasil’shchikov and A.V. Shutov, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 3, pp. 17–23.
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Krasil’shchikov, V.V., Shutov, A.V. Distribution of points of one-dimensional quasilattices with respect to a variable module. Russ Math. 56, 14–19 (2012). https://doi.org/10.3103/S1066369X12030036
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DOI: https://doi.org/10.3103/S1066369X12030036