Flow equivalence of sofic beta-shifts

Rune Johansen

doi:10.1017/etds.2015.81

Flow equivalence of sofic beta-shifts

Rune Johansen^*

^*Corresponding author af dette arbejde

Institut for Matematiske Fag

1 Citationer (Scopus)

Abstract

The Fischer, Krieger, and fiber product covers of sofic beta-shifts are constructed and used to show that every strictly sofic beta-shift is 2-sofic. Flow invariants based on the covers are computed, and shown to depend only on a single integer that can easily be determined from the β-expansion of 1. It is shown that any beta-shift is flow equivalent to a beta-shift given by some 1 < β < 2, and concrete constructions lead to further reductions of the flow classification problem. For each sofic beta-shift, there is an action of Z/2Z on the edge shift given by the fiber product, and it is shown precisely when there exists a flow equivalence respecting these Z/2Z-actions. This opens a connection to ongoing efforts to classify general irreducible 2-sofic shifts via flow equivalences of reducible shifts of finite type (SFTs) equipped with Z/2Z-actions.

Originalsprog	Engelsk
Tidsskrift	Ergodic Theory and Dynamical Systems
Vol/bind	37
Udgave nummer	3
Sider (fra-til)	786-801
Antal sider	16
ISSN	0143-3857
DOI	https://doi.org/10.1017/etds.2015.81
Status	Udgivet - 2017

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10.1017/etds.2015.81

http://arxiv.org/pdf/1504.04966Licens: Andet

Citationsformater

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abstract = "The Fischer, Krieger, and fiber product covers of sofic beta-shifts are constructed and used to show that every strictly sofic beta-shift is 2-sofic. Flow invariants based on the covers are computed, and shown to depend only on a single integer that can easily be determined from the β-expansion of 1. It is shown that any beta-shift is flow equivalent to a beta-shift given by some 1 < β < 2, and concrete constructions lead to further reductions of the flow classification problem. For each sofic beta-shift, there is an action of Z/2Z on the edge shift given by the fiber product, and it is shown precisely when there exists a flow equivalence respecting these Z/2Z-actions. This opens a connection to ongoing efforts to classify general irreducible 2-sofic shifts via flow equivalences of reducible shifts of finite type (SFTs) equipped with Z/2Z-actions.",

author = "Rune Johansen",

year = "2017",

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language = "English",

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AU - Johansen, Rune

PY - 2017

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N2 - The Fischer, Krieger, and fiber product covers of sofic beta-shifts are constructed and used to show that every strictly sofic beta-shift is 2-sofic. Flow invariants based on the covers are computed, and shown to depend only on a single integer that can easily be determined from the β-expansion of 1. It is shown that any beta-shift is flow equivalent to a beta-shift given by some 1 < β < 2, and concrete constructions lead to further reductions of the flow classification problem. For each sofic beta-shift, there is an action of Z/2Z on the edge shift given by the fiber product, and it is shown precisely when there exists a flow equivalence respecting these Z/2Z-actions. This opens a connection to ongoing efforts to classify general irreducible 2-sofic shifts via flow equivalences of reducible shifts of finite type (SFTs) equipped with Z/2Z-actions.

AB - The Fischer, Krieger, and fiber product covers of sofic beta-shifts are constructed and used to show that every strictly sofic beta-shift is 2-sofic. Flow invariants based on the covers are computed, and shown to depend only on a single integer that can easily be determined from the β-expansion of 1. It is shown that any beta-shift is flow equivalent to a beta-shift given by some 1 < β < 2, and concrete constructions lead to further reductions of the flow classification problem. For each sofic beta-shift, there is an action of Z/2Z on the edge shift given by the fiber product, and it is shown precisely when there exists a flow equivalence respecting these Z/2Z-actions. This opens a connection to ongoing efforts to classify general irreducible 2-sofic shifts via flow equivalences of reducible shifts of finite type (SFTs) equipped with Z/2Z-actions.

U2 - 10.1017/etds.2015.81

DO - 10.1017/etds.2015.81

M3 - Journal article

AN - SCOPUS:84955596716

SN - 0143-3857

VL - 37

SP - 786

EP - 801

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 3

ER -

Flow equivalence of sofic beta-shifts

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