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2014 | 126 | 2 | 482-485
Article title

Dynamical Properties of k-Free Lattice Points

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Abstracts
EN
We revisit the visible points of a lattice in Euclidean n-space together with their generalisations, the k-th-power-free points of a lattice, and study the corresponding dynamical system that arises via the closure of the lattice translation orbit. Our analysis extends previous results obtained by Sarnak and by Cellarosi and Sinai for the special case of square-free integers and sheds new light on previous joint work with Peter Pleasants.
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  • Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
author
  • Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
References
  • [1] M. Baake, R.V. Moody, P.A.B. Pleasants, Discrete Math. 221, 3 (2000), doi: 10.1016/S0012-365X(99)00384-2
  • [2] P.A.B. Pleasants, C. Huck, Discrete Comput. Geom. 50, 39 (2013), doi: 10.1007/s00454-013-9516-y
  • [3] J. Kułaga-Przymus, M. Lemańczyk, B. Weiss, preprint, arXiv:1406.3745
  • [4] R. Peckner, preprint, arXiv:1205.2905v7
  • [5] P. Sarnak, Three lectures on the Möbius function randomness and dynamics, Lecture 1, 2010 http://publications.ias.edu/sites/default/files/MobiusFunctionsLectures(2).pdf
  • [6] F. Cellarosi, Ya.G. Sinai, J. Europ. Math. Soc. 15, 1343 (2013), doi: 10.4171/JEMS/394
  • [7] F. Cellarosi, I. Vinogradov, J. Mod. Dyn. 7, 461 (2013), doi: 10.3934/jmd.2013.7.461
  • [8] E.H. el Abdalaoui, M. Lemańczyk, T. de la Rue, preprint, arXiv:1311.3752
  • [9] M. Baake, U. Grimm, Aperiodic Order. Vol. 1. A Mathematical Invitation, Cambridge University Press, Cambridge 2013
  • [10] B. Solomyak, Ergodic Th. & Dynam. Syst. 17, 695 (1997)
  • [11] B. Weiss, Single Orbit Dynamics, AMS, Providence 2000
  • [12] M. Baake, D. Lenz, C. Richard, Lett. Math. Phys. 82, 61 (2007), doi: 10.1007/s11005-007-0186-7
  • [13] E. Akin, The General Topology of Dynamical Systems, AMS, Providence 1993
  • [14] E. Glasner, Ergodic Theory via Joinings, AMS, Providence 2003
  • [15] H. Furstenberg, Math. System Theory 1, 1 (1967), doi: 10.1007/BF01692494
  • [16] P. Walters, An Introduction to Ergodic Theory, reprint, Springer, New York 2000
  • [17] M. Baake, D. Lenz, A. van Enter, Ergodic Th. & Dynam. Syst., in press, arXiv:1307.7518
  • [18] C. Huck, in preparation
  • [19] M. Baake, D. Lenz, Ergodic Th. & Dynam. Syst. 24, 1867 (2004), doi: 10.1017/S0143385704000318
  • [20] B. Sing, Pisot Substitutions and Beyond, Universität Bielefeld, Bielefeld 2006 http://bieson.ub.uni-bielefeld.de/volltexte/2007/1155/
  • [21] M. Baake, D. Lenz, R.V. Moody, Ergodic Th. & Dynam. Syst. 27, 341 (2007), doi: 10.1017/S0143385706000800
Document Type
Publication order reference
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bwmeta1.element.bwnjournal-article-appv126n214kz
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