Limit sets of automatic sequences.
type: Item
instance of: scholarly article
title: Limit sets of automatic sequences.
zbMATH Open document ID: 1050.11026
DOI: 10.1016/S0001-8708(02)00043-9
author: Fritz von Haeseler
author: André Barbé
published in: Advances in Mathematics
publication date: 2003-05-25T00:00:00Z
review text: The authors study the limit sets of multidimensional automatic sequences. For a finite set with a distinguished element \(s_0\), consider an \(\ell\)-dimensional sequence \(f\) in \(S^{\mathbb{N}^\ell}\). A sequence \((t_n)\in\mathbb{N}^{\mathbb{N}}\) is a scaling sequence, if \(({1\over t_n} X(f,t_n))\) is a Cauchy sequence with respect to the Hausdorff distance, where \[ X(f, t_n)= \{Q_\ell+\underline j\mid\|\underline j\|_\infty< t_n,\, f(\underline j)\neq s_0\} \] with \(0\)-dimensional cube \(Q_\ell\). The limit associated with a scaling sequence is a limit set of \(f\). They show that any automatic sequence has natural scaling sequences, and that a limit set of an automatic sequence is a union of primitive limit sets in some sense.
reviewed by: Yuji Kobayashi
Mathematics Subject Classification ID: 11B85
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 37F40
zbMATH DE Number: 1915635
zbMATH Keywords: automatic sequences
zbMATH Keywords: limit set
zbMATH Keywords: self-similarity
MaRDI profile type: Publication
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full work available at URL: s0001-8708(02)00043-9
OpenAlex ID: W2002824538
description: scientific article; zbMATH DE number 1915635