The structure of generalized Morse minimal sets on 𝑛 symbols

Martin, John C.

doi:10.1090/S0002-9947-1977-0463400-1

The structure of generalized Morse minimal sets on $n$ symbols
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Trans. Amer. Math. Soc. 232 (1977), 343-355 Request permission

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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Sur les ensembles minimaux engendres par les substitutions de longueur non constante

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