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}
}