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Topological Entropy Dimension and Directional Entropy Dimension for ℤ2-Subshifts
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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.
Title: Topological Entropy Dimension and Directional Entropy Dimension for ℤ2-Subshifts
Description:
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.
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