A condition for weak mixing of induced IETs (Q2906449)
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scientific article; zbMATH DE number 6077494
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A condition for weak mixing of induced IETs |
scientific article; zbMATH DE number 6077494 |
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A condition for weak mixing of induced IETs (English)
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5 September 2012
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interval exchange transformation
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weak mixing
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induced transformations
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This paper studies properties of ergodic interval exchange transformations (IET). \textit{A. Katok} [Isr. J. Math. 35, 301--310 (1980; Zbl 0437.28009)] showed that IETs are not mixing. However, \textit{A. Avila} and \textit{G. Forni} [Ann. Math. (2) 165, No. 2, 637--664 (2007; Zbl 1136.37003)] showed that almost all IETs with irreducible permutations that are not rotations are weakly mixing. In the paper under review, the author considers an ergodic IET \(f:[0,1) \rightarrow [0,1)\) and defines the set NEWLINE\[NEWLINEX_{\mathrm{wm}} \equiv \{t \in (0,1): f_t \text{ is weakly mixing }\},NEWLINE\]NEWLINE where \(f_t:[0,t) \rightarrow [0,t)\) is the induced IET. The author proves that \(X_{\mathrm{wm}}\) is a residual subset of \([0,1)\) with measure 1.NEWLINENEWLINEFor the entire collection see [Zbl 1237.37004].
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