an:06108790
Zbl 1347.11017
Krasil'shchikov, V. V.; Shutov, A. V.
Distribution of points of one-dimensional quasilattices with respect to a variable module
EN
Russ. Math. 56, No. 3, 14-19 (2012); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2012, No. 3, 17-23 (2012).
00297216
2012
j
11B39 11B83 05B45
one-dimensional quasilattice; Fibonacci tilings; distribution function
Summary: 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.