English

Ergodic properties of {\beta}-adic Halton sequences

Number Theory 2019-02-20 v2

Abstract

We investigate a parametric extension of the classical s-dimensional Halton sequence, where the bases are special Pisot numbers. In a one- dimensional setting the properties of such sequences have already been in- vestigated by several authors [5, 8, 23, 28]. We use methods from ergodic theory to in order to investigate the distribution behavior of multidimen- sional versions of such sequences. As a consequence it is shown that the Kakutani-Fibonacci transformation is uniquely ergodic.

Keywords

Cite

@article{arxiv.1304.2644,
  title  = {Ergodic properties of {\beta}-adic Halton sequences},
  author = {Markus Hofer and Maria Rita Iacò and Robert Tichy},
  journal= {arXiv preprint arXiv:1304.2644},
  year   = {2019}
}
R2 v1 2026-06-21T23:56:41.036Z