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Interval translation mappings

Published online by Cambridge University Press:  14 October 2010

Michael Boshernitzan and
Isaac Kornfeld
Michael Boshernitzan
Affiliation:
Department of Mathematics, Rice University, Houston, Texas 77001, USA
Isaac Kornfeld
Affiliation:
Department of Mathematics, North Dakota State University, Fargo, North Dakota 58105, USA
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Abstract

A class of locally isometric, but not necessarily invertible mappings of an interval is considered. We show that under some conditions the study of the dynamical properties of these mappings can be reduced to interval exchange transformations. On the other hand, there are examples of mappings in this class with ergodic invariant measures supported by Cantor sets. The so-called μβ -sets studied by Y. Katznelson appear naturally in such examples.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 5 , October 1995, pp. 821 - 832
Copyright
Copyright © Cambridge University Press 1995

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