International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 1, Pages 49-54
doi:10.1155/S0161171299220492

Nonwandering sets of maps on the circle

Seung Wha Yeom1 , Kyung Jin Min1 and Seong Hoon Cho3

1Department of Mathematics, Seoul National University of Technology, Nowon-Gu, Seoul 139-743, Korea
 3Department of Mathematics, Hanseo University, Chungnam, Seosan 356-820, Korea

Abstract

Let f be a continuous map of the circle S1 into itself. And let R(f),Λ(f),Γ(f), and Ω(f) denote the set of recurrent points, ω-limit points, γ-limit points, and nonwandering points of f, respectively. In this paper, we show that each point of Ω(f)\R(f)¯ is one-side isolated, and prove that(1) Ω(f)\Γ(f) is countable and(2) Λ(f)\Γ(f) and R(f)¯\Γ(f) are either empty or countably infinite.