Connectedness related to almost periodicity of compositions of flow homomorphisms

D.C. McMahon, J.C.S.P. Woude, van der, T.S. Wu

Research output: Contribution to journalArticleAcademicpeer-review


Consider homomorphisms ϕ : X → Y and ψ : Y → Z, where ϕ is open and N-to-one, ψ is almost periodic. In the paper by R. J Sacker and G. R. Sell, it was shown that, under a certain condition on the phase group, the composition ψ ∘ϕ : X → Z is almost periodic (provided that Z is trivial and X is minimal). In this paper almost periodicity of ψ ∘ ϕ is studied under connectedness conditions on the fibers of ψ. For instance it is shown that if ψ is almost periodic with connected fibers than ψ ⋅ ϕ is almost periodic. If ψ is locally almost periodic with locally connected fibers then ϕ ∘ ψ is locally almost periodic.
Original languageEnglish
Pages (from-to)127-148
Number of pages22
JournalPacific Journal of Mathematics
Issue number1
Publication statusPublished - 1987


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