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Expansive dynamics on locally compact groups

Published online by Cambridge University Press:  18 November 2020

BRUCE P. KITCHENS*
Affiliation:
Indiana University–Purdue University Indianapolis, Indianapolis, IN46202, USA

Abstract

Let $\mathcal {G}$ be a second countable, Hausdorff topological group. If $\mathcal {G}$ is locally compact, totally disconnected and T is an expansive automorphism then it is shown that the dynamical system $(\mathcal {G}, T)$ is topologically conjugate to the product of a symbolic full-shift on a finite number of symbols, a totally wandering, countable-state Markov shift and a permutation of a countable coset space of $\mathcal {G}$ that fixes the defining subgroup. In particular if the automorphism is transitive then $\mathcal {G}$ is compact and $(\mathcal {G}, T)$ is topologically conjugate to a full-shift on a finite number of symbols.

MSC classification

Type
Original Article
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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