Almost every interval translation map of three intervals is finite type (Q379877)
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scientific article; zbMATH DE number 6224729
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Almost every interval translation map of three intervals is finite type |
scientific article; zbMATH DE number 6224729 |
Statements
Almost every interval translation map of three intervals is finite type (English)
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11 November 2013
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interval translation map
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interval exchange transformation
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finite type
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infinite type
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double rotation
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color rotation
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Interval translation maps (ITM) were introduced in [\textit{M. Boshernitzan} and \textit{I. Kornfeld}, Ergodic Theory Dyn. Syst. 15, No. 5, 821--832 (1995; Zbl 0836.58026)], and they are generalizations of interval exchange transformations (IET) in the sense that an ITM may not be invertible.NEWLINENEWLINEAn ITM is said to be of finite type, if after some reductions, it becomes an IET. Boshernitzan and Kornfeld constructed an ITM of infinite type. A natural question is whether most ITMs are of finite type.NEWLINENEWLINEIn this paper the author proves that, among the space of ITMs for three intervals, the set of ITMs of finite type contains an open and dense subset, and is also of full measure.
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