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Abstract

We consider indecomposable inverse limits of certain unimodal maps on intervals, and we use the Axiom of Choice to assign sequences of zeros and ones to points of these spaces so that two points belong to the same composant if and only if their itineraries agree on their tails. This extends results long known to hold for any indecomposable continuum that arises as the inverse limit of a single tent core with a nonrecurrent or periodic critical point. For the context in which the inverse limit is generated by a single unimodal map, it is shown that sequences may be assigned in such a way that the shift on the resulting sequence space is semiconjugate to the shift homeomorphism on the inverse limit.