Abstract
A notion of the pseudo orbit tracing property (abbr. POTP) for oneparameter flows on compact metric spaces is discussed. The strong POTP, the strong finite POTP, the normal POTP, the weak POTP and the finite POTP for flows are defined, and the relation between these POTP's is clarified; these are equivalent to each other for flows with no fixed points, but that is not true for flows with fixed points. Moreover, the following is proved; (i) The restriction to the nonwandering set of a flow with the strong POTP has the strong POTP. (ii) If an expansive flow on the nonwandering set has the finite POTP, the flow splits into the finite union of subsystems with topological transitivity. (iii) Every isometric flow with the finite POTP is minimal. (iv) The direct product of flows with the strong POTP does not necessarily have the finite POTP.
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Komuro, M. One-parameter flows with the pseudo orbit tracing property. Monatshefte für Mathematik 98, 219–253 (1984). https://doi.org/10.1007/BF01507750
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DOI: https://doi.org/10.1007/BF01507750