Cantor Limit Set of a Topological Transformation Group on S1

Keying Guan1 and Zuming Chen2 1 Science College, Northern Jiao Tong University, Beijing 100044, China 2 Science College, Beijing University of Aeronautics and Astronautics, Beijing 100083, China Correspondence should be addressed to Keying Guan, [email protected] Received 15 June 2011; Revised 14 October 2011; Accepted 19 October 2011 Academic Editor: Rutwig Campoamor-Stursberg Copyright q 2011 K. Guan and Z. 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 S1 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.