Disjointness between bounded rank-one transformations

Abstract

In this paper some sufficient conditions are given for when two bounded rank-one transformations are non-isomorphic and when they are disjoint. We also obtain sufficient conditions for a bounded rank-one transformation to have minimal self-joinings. For commensurate, canonically bounded rank-one transformations, isomorphism and disjointness are completely determined by simple conditions in terms of their cutting and spacer parameters.

Dynamical properties of minimal Ferenczi subshifts

“…Moreover, they have non-superlinear symbolic complexity [Fer96, Proposition 2], but they may have peaks with any prescribed sub-exponential growth [Fer96, Proposition 3]. We refer to [AFP17, GH14, GH16a, GH16b, GH21, GZ19, GZ20] for recent results about the combinatorial and topological models of rank-one systems.…”