On directional entropy functions |
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Authors: | Kyewon Koh Park |
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Institution: | (1) Department of Mathematics, Ajou University, 442-749 Suwon, Korea |
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Abstract: | Given aZ
2-process, the measure theoretic directional entropy function,h(
% MathType!End!2!1!), is defined on
% 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.
This research is supported in part by BSRI and KOSEF 95-0701-03-3. |
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Keywords: | |
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