Article

Israel Journal of Mathematics

, Volume 50, Issue 1, pp 160-168

Cutting and stacking, interval exchanges and geometric models

  • Pierre ArnouxAffiliated withU.E.R. Sciences de Reims
  • , Donald S. OrnsteinAffiliated withStanford University
  • , Benjamin WeissAffiliated withThe Hebrew University of Jerusalem

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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.