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Ergodic Theory and Dynamical Systems (1)

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Classification of backward filtrations and factor filtrations: examples from cellular automata
Part of
PAUL LANTHIER, THIERRY DE LA RUE
Journal:

Ergodic Theory and Dynamical Systems / Volume 42 / Issue 9 / September 2022

Published online by Cambridge University Press:

21 July 2021, pp. 2890-2922

Print publication:

September 2022
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We consider backward filtrations generated by processes coming from deterministic and probabilistic cellular automata. We prove that these filtrations are standard in the classical sense of Vershik’s theory, but we also study them from another point of view that takes into account the measure-preserving action of the shift map, for which each sigma-algebra in the filtrations is invariant. This initiates what we call the dynamical classification of factor filtrations, and the examples we study show that this classification leads to different results.