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On the problem of embedding discrete flows in continuous flows. (English) Zbl 0549.58030
Dynamical systems II, Proc. int. Symp., Gainesville/Fla. 1981, 565-568 (1982).
[For the entire collection see Zbl 0532.00014.]
N. E. Foland and W. R. Utz [Ergodic Theory, 121-134 (1963; Zbl 0132.190)] observed that any self-homeomorphism, T, of a topological space, X, can be embedded in a continuous flow on an enlarged space secured by lifting X. Also, that if X is a separable metric space, then the homeomorphism can be embedded in a continuous flow on a Bebutoff space of continuous functions. According to a major theorem of this paper if X is a separable metric space, then these two embeddings are topologically equivalent if, and only if, T has no fixed poins.
As a consequence of a different result the author identifies a class of orientation preserving self-homeomorphisms of the plane with a finite number of fixed points which cannot be embedded in a continuous flow on the plane.
Reviewer: C.Chicone

MSC:
37C10 Dynamics induced by flows and semiflows
54H20 Topological dynamics (MSC2010)