Ergodic Theory and Dynamical Systems

Research Article

Furstenberg’s structure theorem via CHART groups

WARREN B. MOORSa1 and ISAAC NAMIOKAa2

a1 Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand (email: moors@math.auckland.ac.nz)

a2 University of Washington, Department of Mathematics, Box 354350, Seattle, WA 98195-4350, USA (email: namioka@math.washington.edu)

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.

(Received October 03 2011)

(Revised January 10 2012)