Disjoint groups of homeomorphisms of the circle. (English) Zbl 1132.37018
Summary: Let \(G\) be a group of homeomorphisms of the unit circle with respect to composition. In this paper we prove that if \(G\) is disjoint, that is every element of \(G\) either is the identity mapping or has no fixed point, then \(G\) is an iteration group. We also give some sufficient conditions for disjointedness of groups of homeomorphisms of the circle.
MSC:
37E10 | Dynamical systems involving maps of the circle |
39B12 | Iteration theory, iterative and composite equations |
20F38 | Other groups related to topology or analysis |