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Article Dans Une Revue Nonlinearity Année : 2021

RESCALED ENTROPY OF CELLULAR AUTOMATA

Résumé

For a d-dimensional cellular automaton with d ≥ 1 we introduce a rescaled en-tropy which estimates the growth rate of the entropy at small scales by generalizing previous approaches [1, 9]. We also define a notion of Lyapunov exponent and proves a Ruelle inequality as already established for d = 1 in [16, 15]. Finally we generalize the entropy formula for 1-dimensional permutative cellular automata [18] to the rescaled entropy in higher dimensions. This last result extends recent works [17] of Shinoda and Tsukamoto dealing with the metric mean dimensions of two-dimensional symbolic dynamics.
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Dates et versions

hal-02610374 , version 1 (16-05-2020)
hal-02610374 , version 2 (08-07-2020)

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David Burguet. RESCALED ENTROPY OF CELLULAR AUTOMATA. Nonlinearity, 2021. ⟨hal-02610374v2⟩
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