Ergodic properties of {\beta}-adic Halton sequences

摘要

We investigate a parametric extension of the classical s-dimensional Haltonsequence, where the bases are special Pisot numbers. In a one- dimensionalsetting the properties of such sequences have already been in- vestigated byseveral authors [5, 8, 23, 28]. We use methods from ergodic theory to in orderto investigate the distribution behavior of multidimen- sional versions of suchsequences. As a consequence it is shown that the Kakutani-Fibonaccitransformation is uniquely ergodic.