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Smorodinsky’s conjecture on rank-one mixing. (English) Zbl 0906.28006

The author proves Smorodinsky’s conjecture that asserts that the rank-one transformation obtained by adding staircases whose heights increase consecutively by one is mixing. In fact, it is proved that an infinite staircase construction for which \(\lim_{n\to\infty}{r_n\over h_n} =0\) is mixing (\(r_n\) is the sequence of cuts and \(h_n\) the sequence of heights of the staircase construction).

MSC:

28D05 Measure-preserving transformations
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