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Smoothability of Cherry flows on two-manifolds. (English) Zbl 0545.58039

Geometric dynamics, Proc. int. Symp. Rio de Janeiro/Brasil 1981, Lect. Notes Math. 1007, 308-331 (1983).
[For the entire collection see Zbl 0511.00026.]
A continuous flow is smoothable if it is topologically equivalent to a smooth one. The author proves that any continuous Cherry flow [T. M. Cherry, Proc. Lond. Math. Soc., II. Ser. 44, 175-215 (1938; Zbl 0019.11503)] is smoothable. In particular, any continuous flow on a compact two-manifold, with finitely many fixed points and a dense positive semitrajectory, is smoothable.
Reviewer: A.Reinfelds

MSC:

37C10 Dynamics induced by flows and semiflows