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arxiv: 1601.04119 · v1 · pith:DXR5AD5Pnew · submitted 2016-01-16 · 🧮 math.DS

Disjointness between bounded rank-one transformations

classification 🧮 math.DS
keywords boundedrank-onetransformationsconditionsdisjointnessminimalself-joiningssufficient
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In this paper some sufficient conditions are given for when two bounded rank-one transformations are isomorphic or disjoint. For commensurate, canonically bounded rank-one transformations, isomorphism and disjointness are completely determined by simple conditions in terms of their cutting and spacer parameters. We also obtain sufficient conditions for bounded rank-one transformations to have minimal self-joinings. As an application, we give a proof of Ryzhikov's theorem that totally ergodic, non-rigid, bounded rank-one transformations have minimal self-joinings of all orders.

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