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Article

Bowen Lemma in the Countable Symbolic Space

by 1,* and 2
1
College of Mathematics and Informatics, Fujian Normal University, Fuzhou 350117, China
2
Department of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
*
Author to whom correspondence should be addressed.
Entropy 2017, 19(10), 532; https://doi.org/10.3390/e19100532
Received: 14 August 2017 / Revised: 27 September 2017 / Accepted: 30 September 2017 / Published: 11 October 2017
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
We consider the sets of quasi-regular points in the countable symbolic space. We measure the sizes of the sets by Billingsley-Hausdorff dimension defined by Gibbs measures. It is shown that the dimensions of those sets, always bounded from below by the convergence exponent of the Gibbs measure, are given by a variational principle, which generalizes Li and Ma’s result and Bowen’s result. View Full-Text
Keywords: measure theoretic entropy; Gibbs measure; Hausdorff dimension; symbolic dynamical system; Bowen Lemma; quasi-regular point measure theoretic entropy; Gibbs measure; Hausdorff dimension; symbolic dynamical system; Bowen Lemma; quasi-regular point
MDPI and ACS Style

Li, M.; Ma, J. Bowen Lemma in the Countable Symbolic Space. Entropy 2017, 19, 532. https://doi.org/10.3390/e19100532

AMA Style

Li M, Ma J. Bowen Lemma in the Countable Symbolic Space. Entropy. 2017; 19(10):532. https://doi.org/10.3390/e19100532

Chicago/Turabian Style

Li, Mingtian; Ma, Jihua. 2017. "Bowen Lemma in the Countable Symbolic Space" Entropy 19, no. 10: 532. https://doi.org/10.3390/e19100532

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