Publication Date

1-12-2021

Document Type

Article

Organizational Units

College of Natural Science and Mathematics, Mathematics

Keywords

Gibbs bounds, Intrinsic ergodicity, Symbolic dynamics

Abstract

In this work, we treat subshifts, defined in terms of an alphabet A and (usually infinite) forbidden list F, where the number of n-letter words in F has ‘slow growth rate’ in n. We show that such subshifts are well behaved in several ways; for instance, they are boundedly supermultiplicative in the sense of Baker and Ghenciu [Dynamical properties of S-gap shifts and other shift spaces. J. Math. Anal. Appl.430(2) (2015), 633–647] and they have unique measures of maximal entropy with the K-property and which satisfy Gibbs bounds on large (measure-theoretically) sets. The main tool in our proofs is a more general result, which states that bounded supermultiplicativity and a sort of measure-theoretic specification property together imply uniqueness of the measure of maximum entropy and our Gibbs bounds. We also show that some well-known classes of subshifts can be treated by our results, including the symbolic codings of x |-> α + βx (the so-called α-β shifts of Hofbauer [Maximal measures for simple piecewise monotonic transformations. Z. Wahrsch. verw. Geb.52(3) (1980), 289–300]) and the bounded density subshifts of Stanley [Bounded density shifts. Ergod. Th. & Dynam. Sys.33(6) (2013), 1891–1928].

Copyright Statement / License for Reuse

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

Publication Statement

This article was originally published by Cambridge University Press as:

Pavlov, R. (2021). On subshifts with slow forbidden word growth. Ergodic Theory and Dynamical Systems 42(4), 1487-1516. https://doi.org/10.1017/etds.2020.138

Copyright is held by the author. User is responsible for all copyright compliance.

Rights Holder

Ronnie Pavlov

Provenance

Received from author

File Format

application/pdf

Language

English (eng)

Extent

30 pgs

File Size

526 KB

Publication Title

Ergodic Theory and Dynamical Systems

Volume

42

First Page

1487

Last Page

1516

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