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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 generalized Morse minimal sets on $ n$ symbols


Author: John C. Martin
Journal: Trans. Amer. Math. Soc. 232 (1977), 343-355
MSC: Primary 28A65
MathSciNet review: 0463400
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Abstract: A class of bisequences on n symbols is constructed which includes the generalized Morse sequences introduced by Keane. Those which give rise to strictly ergodic sets are characterized, and the spectrum of the shift operator on these systems is investigated. It is shown that in certain cases the shift operator has partly discrete and partly continuous spectrum. The theorems generalize results of Keane on generalized Morse sequences and a theorem of Kakutani regarding a particular strictly transitive sequence on four symbols. Another special case yields information on the spectrum of certain substitution minimal sets.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0463400-1
PII: S 0002-9947(1977)0463400-1
Keywords: Generalized Morse sequence, minimal set, strictly ergodic, shift operator, discrete spectrum, eigenvalue group, continuous spectrum, substitution minimal set
Article copyright: © Copyright 1977 American Mathematical Society