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Furstenberg’s structure theorem via CHART groups

Published online by Cambridge University Press:  17 April 2012

WARREN B. MOORS  and
ISAAC NAMIOKA
WARREN B. MOORS
Affiliation:
Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand (email: moors@math.auckland.ac.nz)
ISAAC NAMIOKA
Affiliation:
University of Washington, Department of Mathematics, Box 354350, Seattle, WA 98195-4350, USA (email: namioka@math.washington.edu)
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Abstract

We give an almost self-contained group theoretic proof of Furstenberg’s structure theorem as generalized by Ellis: each minimal compact distal flow is the result of a transfinite sequence of equicontinuous extensions, and their limits, starting from a flow consisting of a singleton. The groups that we use are CHART groups, and their basic properties are recalled at the beginning of the paper.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 3 , June 2013 , pp. 954 - 968
Copyright
Copyright © 2012 Cambridge University Press

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