Classification of odometers: a short elementary proof

Roman Hric; Miroslav Výbošt'ok

Published: 2022-05-28
Language: EN

Vol. 36 No. 2 (2022)

Classification of odometers: a short elementary proof

Roman Hric

, Miroslav Výbošt'ok

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.

(EN)

Keywords:

odometer , conjugacy , self-conjugacy , classification (EN)

Download files

PDF

Citation rules

Hric, R., & Výbošt'ok, M. (2022). Classification of odometers: a short elementary proof. Annales Mathematicae Silesianae, 36(2), 184–192. Retrieved from https://trrest.vot.pl/ojsus/index.php/AMSIL/article/view/13839

References

L. Block and J. Keesling, A characterization of adding machine maps, Topology Appl. 140 (2004), 151–161.
Google Scholar

J. Buescu and I. Stewart, Liapunov stability and adding machines, Ergodic Theory Dynam. Systems 15 (1995), 271–290.
Google Scholar

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.
Google Scholar

E. Hewitt and K. Ross, Abstract Harmonic Analysis I, 2nd Edition, Springer-Verlag, Berlin-New York, 1979.
Google Scholar

S. Kolyada and L’. Snoha, Minimal dynamical systems, Scholarpedia 4(11):5803 (2009), DOI: 10.4249/scholarpedia.5803.
Google Scholar

M. Výbošt'ok, Classification of Floyd–Auslander systems with fixed pattern, Topology Appl. (2022), DOI: 10.1016/j.topol.2022.108143.
Google Scholar

Roman Hric

roman.hric@umb.sk
https://orcid.org/0000-0001-5901-726X

Affiliation:

Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Slovakia Slovakia

Miroslav Výbošt'ok

Affiliation:

Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Slovakia Slovakia

Vol. 36 No. 2 (2022)
Published: 2022-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

Submit