Cantor limit set of a topological transformation group on \(S^{1}\)
Let \(\Gamma \) be a transformation group on the circle \(S^1\) with two generators which are both homeomorphic transformations onto \(S^1\). A characterization for the limit set of \(\Gamma \) to be totally disconnected and perfect is described in this paper in terms of five technical conditions. A very interesting application is presented for a doubly periodic Riccati equation in the complex domain.
scientific article; zbMATH DE number 6013252
scientific article