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

Part of: Topological dynamics Ergodic theory

Published online by Cambridge University Press:  05 July 2023

DARREN CREUTZ
DARREN CREUTZ*
Affiliation:
Department of Mathematics, US Naval Academy, Annapolis, USA
*
email: creutz@usna.edu
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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.

Keywords

symbolic dynamicsword complexityweak mixingrank-one transformations

MSC classification

Primary: 37B10: Symbolic dynamics
Secondary: 37A25: Ergodicity, mixing, rates of mixing
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 44 , Issue 5 , May 2024 , pp. 1330 - 1366
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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