Abstract
We define the notion of canonical boundedness among rank-1 transformations and use it to characterize the class of bounded rank-1 transformations with trivial centralizer. We also explicitly characterize totally ergodic rank-1 transformations with bounded cutting parameter. Together with a recent result of Ryzhikov, our results provide a simple procedure for determining, purely in terms of the cutting and spacer parameters for the transformation, whether a bounded rank-1 transformation has minimal self-joinings of all orders.
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The first author acknowledges the US NSF grants DMS-0901853 and DMS-1201290 for the support of his research.
The second author acknowledges the US NSF grant DMS-0943870 for the support of his research.
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Gao, S., Hill, A. Bounded rank-1 transformations. JAMA 129, 341–365 (2016). https://doi.org/10.1007/s11854-016-0024-x
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DOI: https://doi.org/10.1007/s11854-016-0024-x