Cutting and stacking, interval exchanges and geometric models
- Cite this article as:
- Arnoux, P., Ornstein, D.S. & Weiss, B. Israel J. Math. (1985) 50: 160. doi:10.1007/BF02761122
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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.