Israel Journal of Mathematics

, Volume 78, Issue 1, pp 131–142

# Simple systems and their higher order self-joinings

• E. Glasner
• B. Host
• D. Rudolph
Article

## Abstract

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.

## Keywords

Simple System Spectral Type Finite Type Distal Extension Ergodic System
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• E. Glasner
• 1
• B. Host
• 2
• D. Rudolph
• 3
1. 1.School of Mathematics Tel Aviv UniversityTel AvivIsrael
2. 2.Dept. Math. Info. Universite d’Aix-Marseille II Case 901Marseille Cedex 9France
3. 3.Department of MathematicsUniversity of MarylandCollege ParkU.S.A.