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Some dynamical properties of continuous semi-flows having topological transitivity. (English) Zbl 1098.37503
Summary: We investigate the dynamical properties of continuous semi-flows having topological transitivity on a compact metric space.The main results are as follows: (1) a continuous semi-flow with topological transitivity and positive Lyapunov stability is an almost periodic minimal flow; (2) a continuous semi-flow is uniformly almost periodic minimal flow if and only if it is topologically ergodic and has positively Lyapunov stable points; (3) a continuous flow with topological transitivity on a closed surface is either chaos in the sense of Takens and Ruelle or uniformly almost periodic minimal flow on Torus.

MSC:
37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
54H15 Transformation groups and semigroups (topological aspects)
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