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
The notion of topological entropy dimension for a
-action has been introduced to measure the subexponential complexity of zero entropy systems. Given a
-action, along with a
-entropy dimension, we also consider a finer notion of directional entropy dimension arising from its subactions. The entropy dimension of a
-action and the directional entropy dimensions of its subactions satisfy certain inequalities. We present several constructions of strictly ergodic
-subshifts of positive entropy dimension with diverse properties of their subgroup actions. In particular, we show that there is a
-subshift of full dimension in which every direction has entropy 0.
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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.
Jung U, Lee J, Koh Park K. Topological Entropy Dimension and Directional Entropy Dimension for ℤ2-Subshifts. Entropy. 2017; 19(2):46.
Jung, Uijin; Lee, Jungseob; Koh Park, Kyewon. 2017. "Topological Entropy Dimension and Directional Entropy Dimension for ℤ2-Subshifts." Entropy 19, no. 2: 46.
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