International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 1, Pages 49-54
Nonwandering sets of maps on the circle
1Department of Mathematics, Seoul National University of Technology, Nowon-Gu, Seoul 139-743, Korea
2Department of Mathematics, Hanseo University, Chungnam, Seosan 356-820, Korea
Received 30 April 1997; Revised 25 July 1997
Copyright © 1999 Seung Wha Yeom et al. 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.
Let be a continuous map of the circle into itself. And let , and denote the set of recurrent points, -limit points, -limit points, and nonwandering points of , respectively. In this paper, we show that each point of is one-side isolated, and prove that
(1) is countable and
(2) and are either empty or countably infinite.