Israel Journal of Mathematics

, Volume 113, Issue 1, pp 243–267

On directional entropy functions


  • Kyewon Koh Park
    • Department of MathematicsAjou University

DOI: 10.1007/BF02780179

Cite this article as:
Park, K.K. Isr. J. Math. (1999) 113: 243. doi:10.1007/BF02780179


Given aZ2-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 aZ2-process to itsR2 suspension. We find a sufficient condition for the continuity of directional entropy function. In particular, this shows that the directional entropy is continuous for aZ2-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 aGδ subset ofS1. We study examples to investigate some properties of directional entropy functions.

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© The Magnes Press 1999