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Keywords = ℤ2-action

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13 pages, 284 KiB  
Article
Topological Entropy Dimension and Directional Entropy Dimension for ℤ2-Subshifts
by Uijin Jung, Jungseob Lee and Kyewon Koh Park
Entropy 2017, 19(2), 46; https://doi.org/10.3390/e19020046 - 24 Jan 2017
Cited by 4 | Viewed by 4799
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Entropic Properties of Dynamical Systems)
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