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Entropy 2017, 19(10), 532; doi:10.3390/e19100532

Bowen Lemma in the Countable Symbolic Space

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.
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)
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Abstract

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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Li, M.; Ma, J. Bowen Lemma in the Countable Symbolic Space. Entropy 2017, 19, 532.

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