Geodesic
Conservation Laws and Invariant Measures in Surjective Cellular Automata
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems, DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems (2011).

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We discuss a close link between two seemingly different topics studied in the cellular automata literature: additive conservation laws and invariant probability measures. We provide an elementary proof of a simple correspondence between invariant full-support Bernoulli measures and interaction-free conserved quantities in the case of one-dimensional surjective cellular automata. We also discuss a generalization of this fact to Markov measures and higher-range conservation laws in arbitrary dimension. As a corollary, we show that the uniform Bernoulli measure is the only shift-invariant, full-support Markov measure that is invariant under a strongly transitive cellular automaton. 
@article{DMTCS_2011_special_261_a0,
     author = {Kari, Jarkko and Taati, Siamak},
     title = {Conservation {Laws} and {Invariant} {Measures} in {Surjective} {Cellular} {Automata}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems},
     year = {2011},
     doi = {10.46298/dmtcs.2968},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2968/}
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Kari, Jarkko; Taati, Siamak. Conservation Laws and Invariant Measures in Surjective Cellular Automata. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems, DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems (2011). doi : 10.46298/dmtcs.2968. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2968/

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