This paper is devoted to an
analysis of the class of minimal sets which are constructed in the following way: Start
with a homeomorphism of the circle without periodic points. It contains a unique
minimal set. Take a finite number of copies of this minimal set. Define a
homeomorphism of this space onto itself by using the original homeomorphism and a
continuous rule to determine in which copy the image lies. Finally some of the pairs
of doubly asymptotic orbits may be identified. In other words, minimal skew
products of a specific kind of minimal cascade and a finite permutation group with
some trivial identification are studied.
