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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.

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References

  1. P. Arnoux,Exchanges d’intervalle et flots sur les surfaces, inThéorie Ergodique, Monographie No. 29 de l’Enseignement Mathématiques, 1980, pp. 5–38.

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Authors and Affiliations

  1. U.E.R. Sciences de Reims, 51062, Reims, France

    Pierre Arnoux

  2. Stanford University, 94305, Stanford, CA, USA

    Donald S. Ornstein

  3. The Hebrew University of Jerusalem, Jerusalem, Israel

    Benjamin Weiss

Authors
  1. Pierre Arnoux
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  2. Donald S. Ornstein
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  3. Benjamin Weiss
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Additional information

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

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Arnoux, P., Ornstein, D.S. & Weiss, B. Cutting and stacking, interval exchanges and geometric models. Israel J. Math. 50, 160–168 (1985). https://doi.org/10.1007/BF02761122

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  • DOI: https://doi.org/10.1007/BF02761122

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