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Word complexity of (measure-theoretically) weakly mixing rank-one subshifts

Published online by Cambridge University Press:  05 July 2023

DARREN CREUTZ*
Affiliation:
Department of Mathematics, US Naval Academy, Annapolis, USA
*

Abstract

We exhibit, for arbitrary $\epsilon> 0$, subshifts admitting weakly mixing (probability) measures with word complexity p satisfying $\limsup p(q) / q < 1.5 + \epsilon $. For arbitrary $f(q) \to \infty $, said subshifts can be made to satisfy $p(q) < q + f(q)$ infinitely often. We establish that every subshift associated to a rank-one transformation (on a probability space) which is not an odometer satisfies $\limsup p(q) - 1.5q = \infty $ and that this is optimal for rank-ones.

Type
Original Article
Copyright
© The Author(s), 2023. Published by Cambridge University Press

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