Israel Journal of Mathematics

, Volume 50, Issue 1, pp 160–168

Cutting and stacking, interval exchanges and geometric models

  • Pierre Arnoux
  • Donald S. Ornstein
  • Benjamin Weiss

DOI: 10.1007/BF02761122

Cite this article as:
Arnoux, P., Ornstein, D.S. & Weiss, B. Israel J. Math. (1985) 50: 160. doi:10.1007/BF02761122


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.

Copyright information

© The Hebrew University 1985

Authors and Affiliations

  • Pierre Arnoux
    • 1
  • Donald S. Ornstein
    • 2
  • Benjamin Weiss
    • 3
  1. 1.U.E.R. Sciences de ReimsReimsFrance
  2. 2.Stanford UniversityStanfordUSA
  3. 3.The Hebrew University of JerusalemJerusalemIsrael