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Characterizations of open and semi-open maps of compact Hausdorff spaces by induced maps
Xiongping Dai, Yuxun Xie
Let be a continuous surjection of compact Hausdorff spaces. By $$f_*\colon\mathfrak{M}(X)\rightarrow\mathfrak{M}(Y),\ μ\mapsto μ\circ f^{-1} \quad{\rm and}…
Veech's Theorem of acting freely on and Structure Theorem of a.a. flows
Xiongping Dai, Hailan Liang, Zhengyu Yin
Veech's Theorem claims that if is a locally compact\,(LC) Hausdorff topological group, then it may act freely on . We prove Veech's Theorem for being only…
On M-dynamics and Li-Yorke chaos of extensions of minimal dynamics
Xiongping Dai
Let be an extension of minimal compact metric flows such that . A subflow of is called an M-flow if…
On recurrence in zero-dimsnional locally compact flow with compactly generated phase group
Xiongping Dai
We define recurrence for a compactly generated para-topological group acting continuously on a locally compact Hausdorff space with , and then, show that if $\ove…
Chaotic dynamics of continuous-time topological semi-flows on Polish spaces
Xiongping Dai
In this paper, we study the chaotic dynamics of a continuous-time topological semi-flow on a Polish space.
Criterion for quasi-anosovian diffeomorphisms of closed manifolds
Xiongping Dai
Quasi-Anosov diffeomorphism is a kind of important dynamical system due to R. Mane 1970s. In this paper, we present a criterion for such dynamics using ergodic theory.