Dimension and measure theoretic entropy of a subshift in symbolic space
type: Item
instance of: scholarly article
title: Dimension and measure theoretic entropy of a subshift in symbolic space
zbMATH Open document ID: 0896.58025
DOI: 10.1007/BF02882845
author: Ercai Chen
author: Jincheng Xiong
published in: Chinese Science Bulletin
publication date: 1997-11-25T00:00:00Z
review text: This short paper establishes a relationship between the Hausdorff dimension and the measure theoretic entropy of any subshift on the symbol space of \(N\) letters. The authors establish as well a variational principle for the Hausdorff dimension in terms of the measure theoretic entropy of ergodic invariant measures. In addition, the authors show that Bowen's formula for the Hausdorff dimension holds even when the assumption of Markov structure is eliminated.
Mathematics Subject Classification ID: 37E99
Mathematics Subject Classification ID: 28D20
Mathematics Subject Classification ID: 37A99
zbMATH DE Number: 1091413
zbMATH Keywords: symbolic space
zbMATH Keywords: subshift
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: measure theoretic entropy
reviewed by: William J. Satzer Jr.
MaRDI profile type: Publication
cites work: Q3931654
cites work: Dimension, entropy and Lyapunov exponents
cites work: Intersecting random translates of invariant Cantor sets
cites work: Dimensions and Measures of Quasi Self-Similar Sets
description: scientific article; zbMATH DE number 1091413