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Measure-Theoretically Mixing Subshifts with Low Complexity by Creutz, Darren; Pavlov, Ronnie; Rodock, Shaun is a scholarly article available to read on EtoBox.

What is Measure-Theoretically Mixing Subshifts with Low Complexity about?

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 $f : \mathbb{N} \to \mathbb{N}$ with $f(n)/n$ increasing and $\sum 1/f(n) < \infty$, 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.

Author

Creutz, Darren; Pavlov, Ronnie; Rodock, Shaun

Published

2022

Language

EN