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Entropy 2017, 19(2), 46; doi:10.3390/e19020046

Topological Entropy Dimension and Directional Entropy Dimension for ℤ2-Subshifts

Department of Mathematics, Ajou University, 206 Worldcup-ro, Suwon 16499, Korea
School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 02455, Korea
Author to whom correspondence should be addressed.
Academic Editor: Tomasz Downarowicz
Received: 29 November 2016 / Revised: 11 January 2017 / Accepted: 12 January 2017 / Published: 24 January 2017
(This article belongs to the Special Issue Entropic Properties of Dynamical Systems)
View Full-Text   |   Download PDF [284 KB, uploaded 3 February 2017]


The notion of topological entropy dimension for a Z -action has been introduced to measure the subexponential complexity of zero entropy systems. Given a Z 2 -action, along with a Z 2 -entropy dimension, we also consider a finer notion of directional entropy dimension arising from its subactions. The entropy dimension of a Z 2 -action and the directional entropy dimensions of its subactions satisfy certain inequalities. We present several constructions of strictly ergodic Z 2 -subshifts of positive entropy dimension with diverse properties of their subgroup actions. In particular, we show that there is a Z 2 -subshift of full dimension in which every direction has entropy 0. View Full-Text
Keywords: 2-action; entropy dimension; directional entropy dimension; entropy generating shape; minimal 2-action; entropy dimension; directional entropy dimension; entropy generating shape; minimal
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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Jung, U.; Lee, J.; Koh Park, K. Topological Entropy Dimension and Directional Entropy Dimension for ℤ2-Subshifts. Entropy 2017, 19, 46.

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