Abstract
Let π:X→Y be an extension of minimal compact flows such that Rπ≠ΔX. A subflow of Rπ is called an M-flow if it is T.T. and contains a dense set of a.p. points. In this paper we mainly prove the following:(1)π is PI iff ΔX is the unique M-flow containing ΔX in Rπ.(2)If X is a compact metric space and π is not PI, then there exists a canonical Li-Yorke chaotic M-flow in Rπ. In particular, an Ellis weak-mixing non-proximal metric extension is non-PI and so Li-Yorke chaotic. In addition, we show(3)a unbounded or non-minimal M-flow, not necessarily compact, is sensitive; and(4)every syndetically distal compact flow is pointwise Bohr a.p.
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