Disjointness between bounded rank-one transformations

Su Gao; Aaron Hill

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arXiv · 1601.04119

Disjointness between bounded rank-one transformations

Su Gao·Aaron Hill

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Abstract

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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Su Gao, Aaron Hill. 2016-01-16. Disjointness between bounded rank-one transformations. https://arxiv.org/abs/1601.04119

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