Cutting and stacking, interval exchanges and geometric models

Pierre Arnoux; Donald S. Ornstein; Benjamin Weiss

doi:10.1007/BF02761122

Cutting and stacking, interval exchanges and geometric models

Pierre Arnoux^*, Donald S. Ornstein, Benjamin Weiss

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

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 a C^∞-flow on an open 2-manifold. Several additional applications of the basic theorems are also given.

Original language	English
Pages (from-to)	160-168
Number of pages	9
Journal	Israel Journal of Mathematics
Volume	50
Issue number	1-2
DOIs	https://doi.org/10.1007/BF02761122
State	Published - Mar 1985

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title = "Cutting and stacking, interval exchanges and geometric models",

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 a C ∞-flow on an open 2-manifold. Several additional applications of the basic theorems are also given.",

author = "Pierre Arnoux and Ornstein, {Donald S.} and Benjamin Weiss",

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AB - 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 a C ∞-flow on an open 2-manifold. Several additional applications of the basic theorems are also given.

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Cutting and stacking, interval exchanges and geometric models

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