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Dynamical Properties of Certain Open, Topologically Mixing and Strongly Transitive CA
Wit Foryś and Janusz Matyja

In our previous papers we proved that those cellular automata〈CA〉in the metric Cantor space à whose topological entropies form the set P = {log p : p is a prime number} and which are a base of our constructions of one-sided right-closing, open, topologically mixing and strongly transitive CA in Ã𝕄, where either 𝕄 = ℕ or 𝕄 = ℤ, are not topologically conjugate to their column subhifts which are one-sided topologically mixing, vertex SFT defined by matrices. In this paper we prove that the increase in the value of the prime number p is accompanied by the increase in the size of the total column amalgamations of two associated matrices which define non topologically conjugate canonical factors of such two non topologically conjugate CA in à with the same topological entropy log p. Additionally, for any prime number p, associated in this way one-sided vertex SFT are not topologically conjugate to one-sided full shifts. Moreover, any two associated in a similar way column subshifts are also not topologically conjugate, and any of them is not topologically conjugate to infinite subset of column subshifts of its CA.

Keywords: Cellular automata, symbolic dynamics, column subshifts, canonical factors, topological conjugacy.

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