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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The structure of substitution minimal sets


Authors: Ethan M. Coven and Michael S. Keane
Journal: Trans. Amer. Math. Soc. 162 (1971), 89-102
MSC: Primary 54.82; Secondary 28.00
MathSciNet review: 0284995
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Abstract: Substitutions of constant length on two symbols and their corresponding minimal dynamical systems are divided into three classes: finite, discrete and continuous. Finite substitutions give rise to uninteresting systems. Discrete substitutions yield strictly ergodic systems with discrete spectra, whose topological structure is determined precisely. Continuous substitutions yield strictly ergodic systems with partly continuous and partly discrete spectra, whose topological structure is studied by means of an associated discrete substitution. Topological and measure-theoretic isomorphisms are studied for discrete and continuous substitutions, and a complete topological invariant, the normal form of a substitution, is given.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0284995-1
PII: S 0002-9947(1971)0284995-1
Keywords: Shift dynamical system, n-adic system, strict ergodicity, substitution, substitution minimal set, structure system, group system, normal form
Article copyright: © Copyright 1971 American Mathematical Society