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Simple systems and their higher order self-joinings

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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.

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Authors and Affiliations

  1. School of Mathematics Tel Aviv University, 69978, Tel Aviv, Israel

    E. Glasner

  2. Dept. Math. Info. Universite d’Aix-Marseille II Case 901, 163, avenue de Luminy-13288, Marseille Cedex 9, France

    B. Host

  3. Department of Mathematics, University of Maryland, 20742, College Park, MD, U.S.A.

    D. Rudolph

Authors
  1. E. Glasner
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  2. B. Host
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  3. D. Rudolph
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Glasner, E., Host, B. & Rudolph, D. Simple systems and their higher order self-joinings. Israel J. Math. 78, 131–142 (1992). https://doi.org/10.1007/BF02801575

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  • DOI: https://doi.org/10.1007/BF02801575

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