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The structure of strongly stationary systems

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Abstract

Motivated by a problem in ergodic Ramsey theory, Furstenberg and Katznelson introduced the notion of strong stationarity, showing that certain recurrence properties hold for arbitrary measure preserving systems if they are valid for strongly stationary ones. We construct some new examples and prove a structure theorem for strongly stationary systems. The building blocks are Bernoulli systems and rotations on nilmanifolds.

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  1. Department of Mathematics McAllister Building, Pennsylvania State University, 16802, University Park, PA, USA

    Nikos Frantzikinakis

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  1. Nikos Frantzikinakis
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Correspondence to Nikos Frantzikinakis.

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Frantzikinakis, N. The structure of strongly stationary systems. J. Anal. Math. 93, 359–388 (2004). https://doi.org/10.1007/BF02789313

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  • DOI: https://doi.org/10.1007/BF02789313

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