He, Lianfa; Gao, Yinghui; Yang, Fenghong Some dynamical properties of continuous semi-flows having topological transitivity. (English) Zbl 1098.37503 Chaos Solitons Fractals 14, No. 8, 1159-1167 (2002). 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. Cited in 7 Documents MSC: 37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) 54H15 Transformation groups and semigroups (topological aspects) Keywords:Continuous semi-flow; Topologically transitive; Lyapunov stable; Topologically; ergodic; Almost periodic point; Chaos in the sense of Takens and Ruelle PDFBibTeX XMLCite \textit{L. He} et al., Chaos Solitons Fractals 14, No. 8, 1159--1167 (2002; Zbl 1098.37503) Full Text: DOI References: [1] Birkhoff, G. D., Dynamical systems (1927), AMS: AMS Providence, RI · Zbl 0171.05402 [2] Li, T. Y.; Yorke, J. A., Period three implies chaos, Amer. Math. Monthly, 82, 985-992 (1975) · Zbl 0351.92021 [3] Auslander, J.; Yorke, J. A., Interval maps, fractors of maps and chaos, Tôboku Math. J., 32, 177-188 (1980) · Zbl 0448.54040 [4] Yang, R. S., Topological ergodic maps (Chinese), Acta. Math. Sinica, 6, 1063-1068 (2001) · Zbl 1012.37007 [5] Nemytskii, V. V.; Stepanov, V. V., Qualitative theory of differential equations (1989), Dover: Dover New York · Zbl 0089.29502 [6] Vellekoop, M.; Berglund, R., On intervals, transitivity=chaos, Amer. Math. Monthly, 101, 4, 353-355 (1994) · Zbl 0886.58033 [7] Aranson, S.; Belitsky, G.; Zhuzhoma, E., Introduction to the qualitative theory of dynamical systems on surfaces, Trans. Math. Monographs, 153 (1996) · Zbl 0853.58090 [8] Ding, T. R., An ergodic theorem for flows on closed surfaces, Nonlinear Anal., 35, 669-676 (1999) · Zbl 0918.58043 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.