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A characterization of uniquely ergodic interval exchange maps in terms of the Jacobi-Perron algorithm. (English) Zbl 0877.11044

A map \(T\) is said to be interval exchanging provided that it is defined on \([0,1)\) and it exchanges the intervals \([0,\alpha)\) and \([\alpha,1)\) for some irrational \(\alpha\). An interval exchanging map satisfies Keane’s infinite orbit condition (i.o.c.) if the \(T\)-orbits of the \(T\)-discontinuities are infinite and distinct. The main result of the paper is a characterization of uniquely ergodic maps among all interval exchanging maps that satisfy i.o.c.

MSC:

11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
28D05 Measure-preserving transformations
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