Nonwandering sets of maps on the circle

Seung Wha Yeom, Kyung Jin Min and Seong-Hoon Cho ()

International Journal of Mathematics and Mathematical Sciences, 1999, vol. 22, 1-6

Abstract:

Let f be a continuous map of the circle S 1 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.

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:365320

DOI: 10.1155/S0161171299220492

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