Vol. 47, No. 1, 1973

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Locally circular minimal sets

Nelson Groh Markley

Vol. 47 (1973), No. 1, 177–197

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.

Mathematical Subject Classification 2000
Primary: 54H20
Received: 28 January 1972
Revised: 13 June 1972
Published: 1 July 1973
Nelson Groh Markley