Classification of Odometers: A Short Elementary Proof

Roman Hric; Miroslav Výbošťok

doi:10.2478/amsil-2022-0010

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Classification of Odometers: A Short Elementary Proof

Annales Mathematicae Silesianae

Volume 36 (2022): Issue 2 (September 2022)

By: Roman Hric and Miroslav Výbošťok

Open Access

|May 2022

Abstract

The paper deals with odometers (i.e. adding machines) of general type. We give a characterization of self-conjugacies of odometers which enables us to present an elementary proof of a classification of odometers given by Buescu and Stewart in [2]. The paper might also serve as a very quick introduction to odometers.

References

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[2] J. Buescu and I. Stewart, Liapunov stability and adding machines, Ergodic Theory Dynam. Systems 15 (1995), 271–290.10.1017/S0143385700008373
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[3] T. Downarowicz, Survey of odometers and Toeplitz flows, in: S. Kolyada et al. (eds.), Algebraic and Topological Dynamics, Contemp. Math., 385, Amer. Math. Soc., Providence, RI, 2005, pp. 7–37.10.1090/conm/385/07188
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[6] M. Výbošťk, Classification of Floyd–Auslander systems with fixed pattern, Topology Appl. (2022), DOI: 10.1016/j.topol.2022.108143.10.1016/j.topol.2022.108143
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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2022-0010 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 184 - 192

Submitted on: Jan 18, 2022

Accepted on: May 12, 2022

Published on: May 28, 2022

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

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© 2022 Roman Hric, Miroslav Výbošťok, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 36 (2022): Issue 2 (September 2022)