대한수학회지 (Journal of the Korean Mathematical Society)
- 제32권3호
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- Pages.573-582
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- 1995
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
Continuity of directional entropy for a class of $Z^2$ -actions
초록
J.Milnor[Mi2] has introduced the notion of directional entropy in his study of Cellular Automata. Cellular Automaton map can be considered as a continuous map from a space $K^Z^n$ to itself which commute with the translation of the lattice $Z^n$. Since the space $K^Z^n$ is compact, map S is uniformly continuous. Hence S is a block map(a finite code)[He]. (S is said to have a finite memory.) In the case of n = 1, we have a shift map, T on $K^Z$, and a block map S and they together generate a $Z^2$ action.