Remarques sur les systemes dynamiques donnes avec plusieurs facteurs
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Two Bernoulli shifts are given, (X, T) and (X′, T′), with independent generatorsR=P ∨Q andR′=P′ ∨Q′ respectively. (R andR′ are finite). One can chooseR such that if (X′, T′) can be made a factor of (X, T) in such a way that (P′) T′ and (Q′) T′ are full entropy factors of (P) T and (Q) T respectively thend (P ∨Q)=d(P′ ∨Q′). In addition it is proved that if (X, T) is a Bernoulli shift and ifS is a measure preserving transformation ofX that has the same factor algebras asT thenS=T orS=T −1. A tool for this proof, which may be of independent interest is a relative version for very weak Bernoullicity.
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