Remarques sur les systemes dynamiques donnes avec plusieurs facteurs |
| |
Authors: | Jean-Paul Thouvenot |
| |
Institution: | (1) Laboratoire de Probabilités, Université de Paris VI - Tour 56, 4, Place Jussieu, 75230 Paris Cedex 05, France |
| |
Abstract: | 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.
Equipe de Recherche no 1 “Processus stochastique et applications” dépendant de la Section no 1 “Mathématiques, Informatique” associée au C.N.R.S. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|