On the embeddability of commuting functions in a flow. (English) Zbl 0797.39007

Zdun, Marek Cezary

Grazer Math. Ber. 316, 201-212 (1992).

Let \(I\) be an open interval and \(f,g:I \to I\) two commuting homeomorphisms without fixed points. A flow is a family of homeomorphisms \(f^ t\) of \(I\) such that \(f^ t \circ f^ s = f^{t+s}\) for all \(t,s\) in \(\mathbb{R}\). The flow is disjoint if all \(f^ t\) which differ from the identity are fixed point-free. The flow is continuous if it is continuous in \(t\) for each fixed \(x\).
The author gives a necessary and sufficient condition for the embeddability of given commuting homeomorphisms \(f,g\) in a disjoint flow. He shows how to construct all solutions of this problem and also considers the embedding of \(f,g\) in a continuous flow.

Reviewer: I.N.Baker (London)

MSC:

39B12	Iteration theory, iterative and composite equations
37C10	Dynamics induced by flows and semiflows
37B99	Topological dynamics

Keywords:

iteration; fixed points; flow; embeddability; continuous flow