, Volume 50, Issue 1-2, pp 160-168

Cutting and stacking, interval exchanges and geometric models

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Abstract

Every aperiodic measure-preserving transformation can be obtained by a cutting and stacking construction. It follows that all such transformations are infinite interval exchanges. This in turn is used to represent any ergodic measure-preserving flow as aC -flow on an open 2-manifold. Several additional applications of the basic theorems are also given.

Partial support for this work was given by the National Science Foundation under grant number MCS81-07092.