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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.

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