Hausdorff dimension of a chaotic set of shift of a symbolic space
type: Item
instance of: scholarly article
title: Hausdorff dimension of a chaotic set of shift of a symbolic space
zbMATH Open document ID: 0843.58041
author: Jincheng Xiong
published in: Science in China. Series A
publication date: 1996-08-21T00:00:00Z
review text: The main result: Let \(\sigma\) be the shift on the space \(\Sigma_N\) of \(N\) symbols. Then there is a set \(A\subset \Sigma_N\) with Hausdorff dimension 1 such that, for any subset \(\varphi\neq B\subset A\), and any continuous map \(F: B\to \Sigma_N\), there is an increasing sequence \(\{ r(n) \}\) of positive integers such that \(\lim_{n\to \infty} \sigma^{r (n)}= F\) pointwise on \(B\); here \(\sigma^i\) denotes the \(i\)-th iterate of \(\sigma\).
Mathematics Subject Classification ID: 37E99
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 26A18
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 786399
zbMATH Keywords: symbolic dynamics
zbMATH Keywords: chaos
zbMATH Keywords: Hausdorff dimension
reviewed by: Jaroslav Smítal
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 786399