International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 342759, 11 pages
Research Article

Cantor Limit Set of a Topological Transformation Group on S1

1Science College, Northern Jiao Tong University, Beijing 100044, China
2Science College, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

Received 15 June 2011; Revised 14 October 2011; Accepted 19 October 2011

Academic Editor: Rutwig Campoamor-Stursberg

Copyright © 2011 Keying Guan and Zuming Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The limit set of a topological transformation group on 𝐒 1 generated by two generators is proved to be totally disconnected (or thin) and perfect if the conditions (i–v) are satisfied. A concrete application to a Doubly Periodic Riccati equation is given.