Dynamical properties of $k$-free lattice points

@article{Huck2014DynamicalPO,
  title={Dynamical properties of \$k\$-free lattice points},
  author={C. Huck and M. Baake},
  journal={Acta Physica Polonica A},
  year={2014},
  volume={126},
  pages={482-485}
}
  • C. Huck, M. Baake
  • Published 2014
  • Physics, Mathematics
  • Acta Physica Polonica A
  • 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. 
    8 Citations

    Figures from this paper.

    Ergodic properties of visible lattice points
    • 31
    • PDF
    Ergodic properties of visible lattice points
    • 1
    Almost Periodic Measures and Meyer Sets
    • 22
    • PDF
    $\mathfrak{B}$-free integers in number fields and dynamics
    • 1
    • PDF
    B-free sets and dynamics
    • 18
    • PDF
    $\mathscr{B}$-free sets and dynamics
    • 8
    • PDF

    References

    SHOWING 1-10 OF 25 REFERENCES
    Diffraction from visible lattice points and kth power free integers
    • 77
    • PDF
    Entropy and Diffraction of the $$k$$k-Free Points in $$n$$n-Dimensional Lattices
    • 37
    • Highly Influential
    • PDF
    Dynamics of self-similar tilings
    • 296
    • PDF
    Characterization of model sets by dynamical systems
    • 102
    • PDF
    Ergodic properties of square-free numbers
    • 51
    • Highly Influential
    • PDF
    Dynamical systems on translation bounded measures: Pure point dynamical and diffraction spectra
    • 144
    • PDF
    Ergodic Theory via Joinings
    • 524
    • PDF
    The general topology of dynamical systems
    • 179