On M-dynamics and Li-Yorke chaos of extensions of minimal dynamics
| Autor: | Dai, Xiongping |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $\pi\colon\mathscr{X}\rightarrow\mathscr{Y}$ be an extension of minimal compact metric flows such that $\texttt{R}_\pi\not=\Delta_X$. A subflow of $\texttt{R}_\pi$ 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) $\pi$ is PI iff $\Delta_X$ is the unique M-flow containing $\Delta_X$ in $\texttt{R}_\pi$. (2) If $\pi$ is not PI, then there exists a canonical Li-Yorke chaotic M-flow in $\texttt{R}_\pi$. In particular, an Ellis weak-mixing non-proximal extension is non-PI and so Li-Yorke chaotic. (3) A unbounded or non-minimal M-flow, not necessarily compact, is sensitive on initial conditions. (4) every syndetically distal flow is pointwise Bohr a.p. Comment: 28 pages and to appear in JDE |
| Databáze: | arXiv |
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