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On directional entropy functions

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Abstract

Given aZ 2-process, the measure theoretic directional entropy function,h(\(\vec v\)% MathType!End!2!1!), is defined on\(S^1 = \left\{ {\vec v:\left\| {\vec v} \right\| = 1} \right\} \subset R^2 \)% MathType!End!2!1!. We relate the directional entropy of aZ 2-process to itsR 2 suspension. We find a sufficient condition for the continuity of directional entropy function. In particular, this shows that the directional entropy is continuous for aZ 2-action generated by a cellular automaton; this finally answers a question of Milnor [Mil]. We show that the unit vectors whose directional entropy is zero form aG δ subset ofS 1. We study examples to investigate some properties of directional entropy functions.

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Authors and Affiliations

  1. Department of Mathematics, Ajou University, 442-749, Suwon, Korea

    Kyewon Koh Park

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  1. Kyewon Koh Park
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This research is supported in part by BSRI and KOSEF 95-0701-03-3.

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Park, K.K. On directional entropy functions. Isr. J. Math. 113, 243–267 (1999). https://doi.org/10.1007/BF02780179

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  • DOI: https://doi.org/10.1007/BF02780179

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