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The measure-theoretic entropy of linear cellular automata with respect to a Markov measure. (English) Zbl 1232.28017

Summary: The purpose of this short paper is to compute the measure-theoretic entropy of the one-dimensional linear cellular automata defined by bipermutative local rules on the ring \(\mathbb Z_m, m \geq 2\), with respect to a Markov measure generated by a stochastic matrix \(P\) and a probability vector \(\pi \) such that \(\pi P = \pi \).

MSC:

28D20 Entropy and other invariants
37A35 Entropy and other invariants, isomorphism, classification in ergodic theory
37B40 Topological entropy
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