Random \(\beta\)-expansions with deleted digits
type: Item
instance of: scholarly article
title: Random \(\beta\)-expansions with deleted digits
zbMATH Open document ID: 1119.37004
published in: Discrete and Continuous Dynamical Systems
publication date: 2007-08-13T00:00:00Z
review text: Let \(\beta>1\) be a real number, and let \(A=\{a_1,\dots,a_m\}\) a given set of real numbers with \(a_1<\dots<a_m\) (\(m\geq 2\)). The authors define random \(\beta\)-expansions of the form \(x=\sum_{i=1}^\infty b_i/\beta^i\), with \(b_i\in A\). The author generalize the results obtained in [J. Eur. Math. Soc. 7, No.~1, 51--68 (2005; Zbl 1074.28008)] to a wider class of digit sets. By sketching a dynamical way of generating the greedy expansion, they give simple dynamical proofs of some of the results proved by \textit{M. Pedicini} in [Theor. Comput. Sci. 332, No.~1--3, 313--336 (2005; Zbl 1080.11009)]. They also generalize the greedy and lazy expansions and define a function \(K\) that generates essentially all \(\beta\)-expansions with digits belonging to the set \(A\). The authors also find a \(K\)-invariant measure such that \((K,\nu)\) is isomorphic to the uniform Bernoulli shift with digit set \(A\).
reviewed by: Takao Komatsu
Mathematics Subject Classification ID: 37A05
Mathematics Subject Classification ID: 11K55
zbMATH DE Number: 5178926
zbMATH Keywords: greedy expansions
zbMATH Keywords: lazy expansions
zbMATH Keywords: Bernoulli shifts
author: K. Dajani
author: C. Kalle
MaRDI profile type: Publication
full work available at URL: dcds.2007.18.199
OpenAlex ID: W2130454515
DOI: 10.3934/DCDS.2007.18.199
description: scientific article; zbMATH DE number 5178926