Flow equivalence of sofic beta-shifts

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Flow equivalence of sofic beta-shifts. / Johansen, Rune.

In: Ergodic Theory and Dynamical Systems, Vol. 37, No. 3, 2017, p. 786-801.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Johansen, R 2017, 'Flow equivalence of sofic beta-shifts', Ergodic Theory and Dynamical Systems, vol. 37, no. 3, pp. 786-801. https://doi.org/10.1017/etds.2015.81

APA

Johansen, R. (2017). Flow equivalence of sofic beta-shifts. Ergodic Theory and Dynamical Systems, 37(3), 786-801. https://doi.org/10.1017/etds.2015.81

Vancouver

Johansen R. Flow equivalence of sofic beta-shifts. Ergodic Theory and Dynamical Systems. 2017;37(3):786-801. https://doi.org/10.1017/etds.2015.81

Author

Johansen, Rune. / Flow equivalence of sofic beta-shifts. In: Ergodic Theory and Dynamical Systems. 2017 ; Vol. 37, No. 3. pp. 786-801.

Bibtex

@article{537ebbaaf07049d7bab4d91eaae7e895,
title = "Flow equivalence of sofic beta-shifts",
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",
doi = "10.1017/etds.2015.81",
language = "English",
volume = "37",
pages = "786--801",
journal = "Ergodic Theory and Dynamical Systems",
issn = "0143-3857",
publisher = "Cambridge University Press",
number = "3",

}

RIS

TY - JOUR

T1 - Flow equivalence of sofic beta-shifts

AU - Johansen, Rune

PY - 2017

Y1 - 2017

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

VL - 37

SP - 786

EP - 801

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 3

ER -

ID: 196167124