Simple systems and their higher order self-joinings
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The purpose of this work is to study the joinings of simple systems. First the joinings of a simple system with another ergodic system are treated; then the pairwise independent joinings of three systems one of which is simple. The main results obtained are: (1) A weakly mixing simple system with no non-trivial factors with absolutely continuous spectral type is simple of all orders. (2) A weakly mixing system simple of order 3 is simple of all orders.
KeywordsSimple System Spectral Type Finite Type Distal Extension Ergodic System
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- [K]J. King,Ergodic properties where order 4 implies infinite order, Israel J. Math., to appear.Google Scholar