On M-dynamics and Li-Yorke chaos of extensions of minimal dynamics

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