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Symbolic dynamics, Word complexity, Strong mixing, Rank-one transformations

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College of Natural Science and Mathematics, Mathematics


We introduce a class of rank-one transformations, which we call extremely elevated staircase transformations. We prove that they are measure-theoretically mixing and, for any f : N → N with f (n)/n increasing and ∑ 1/f (n) < ∞, that there exists an extremely elevated staircase with word complexity p(n) = o(f (n)). This improves the previously lowest known complexity for mixing subshifts, resolving a conjecture of Ferenczi.

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This article was originally published as:

Creutz, D., Pavlov, R., & Rodock, S. (2022). Measure-theoretically mixing subshifts with low complexity. Ergodic Theory and Dynamical Systems, 1-24. doi:10.1017/etds.2022.42

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Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.