A generic distal tower of arbitrary countable height over an arbitrary infinite ergodic system

Eli Glasner; Benjamin Weiss

doi:10.3934/jmd.2021015

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2021, Volume 17: 435-463. Doi: 10.3934/jmd.2021015

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A generic distal tower of arbitrary countable height over an arbitrary infinite ergodic system

Eli Glasner^1, and
Benjamin Weiss^2,

1.
Department of Mathematics, Tel Aviv University, Tel Aviv 69978, Israel
2.
Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

Received: June 25, 2020

Revised: July 08, 2021

Published: November 2021

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Abstract

We show the existence, over an arbitrary infinite ergodic $ \mathbb{Z} $-dynamical system, of a generic ergodic relatively distal extension of arbitrary countable rank and arbitrary infinite compact extending groups (or more generally, infinite quotients of compact groups) in its canonical distal tower.

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Mathematics Subject Classification: 37A05, 37A20.

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References

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