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Cutting and stacking, interval exchanges and geometric models. (English) Zbl 0558.58019
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 is used to represent any ergodic measure-preserving flow as a \(C^{\infty}\)-flow on an open 2-manifold. Several additional applications of the basic theorems are also given.

MSC:
37A99 Ergodic theory
58C35 Integration on manifolds; measures on manifolds
28D05 Measure-preserving transformations
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