Bounded rank-1 transformations. (English) Zbl 1376.37006
Summary: 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 V. V. Ryzhikov [“Minimal self-joinings, bounded constructions, and weak closure of ergodic actions”, Preprint, arXiv:1212.2602], 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.
MSC:
| 37A25 | Ergodicity, mixing, rates of mixing |
| 54H05 | Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) |
References:
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