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- W1587226223 abstract "We show that for an additive one-dimensional cellular automaton (CA) Z2-action Φ on the space of all doubly infinite sequences with values in a finite set Za={0,1,2,…,a-1}, determined by an additive automaton rule F(xn-k,…,xn+k)=∑i=-kkλixn+i(moda), and a Φ-invariant uniform Bernoulli measure, the directional entropy is hv→(Φ)=2k2loga for v→=(k1,k2)∈Z+2, where k2 > k1 and λi∈Za. We also calculate the measure-theoretic entropy for additive CA Z×N-actions Φ generated by some additive one-dimensional cellular automata and shift transformation and we show that uniform Bernoulli measure is a maximal measure for additive CA Z×N-actions Φ." @default.
- W1587226223 created "2016-06-24" @default.
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- W1587226223 date "2005-11-01" @default.
- W1587226223 modified "2023-09-29" @default.
- W1587226223 title "On the directional entropy of -actions generated by additive cellular automata" @default.
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- W1587226223 doi "https://doi.org/10.1016/j.amc.2004.11.032" @default.
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