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Ergodic properties of $\beta $-adic Halton sequences

Published online by Cambridge University Press:  11 October 2013

MARKUS HOFER ,
MARIA RITA IACÒ  and
ROBERT TICHY
MARKUS HOFER
Affiliation:
Johannes Kepler University, Institute of Financial Mathematics, Altenbergerstrasse 69, 4040 Linz, Austria email markus.hofer@tugraz.at
MARIA RITA IACÒ
Affiliation:
Graz University of Technology, Institute of Mathematics A, Steyrergasse 30, 8010 Graz, Austria email iaco@math.tugraz.attichy@tugraz.at University of Calabria, Department of Mathematics and Computer Science, Via P. Bucci 30B, 87036 Arcavacata di Rende (CS), Italy email iaco@math.tugraz.at
ROBERT TICHY
Affiliation:
Graz University of Technology, Institute of Mathematics A, Steyrergasse 30, 8010 Graz, Austria email iaco@math.tugraz.attichy@tugraz.at
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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 investigated by several authors. We use methods from ergodic theory in order to investigate the distribution behavior of multidimensional versions of such sequences. As a consequence it is shown that the Kakutani–Fibonacci transformation is uniquely ergodic.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 3 , May 2015 , pp. 895 - 909
Copyright
© Cambridge University Press, 2013 

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