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Open AccessArticle

Topological Entropy Dimension and Directional Entropy Dimension for ℤ2-Subshifts

1
Department of Mathematics, Ajou University, 206 Worldcup-ro, Suwon 16499, Korea
2
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
Entropy 2017, 19(2), 46; https://doi.org/10.3390/e19020046
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)
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
MDPI and ACS Style

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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