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The Set of ω‐Limit Points of A Map of the Circle is Closed

 

作者: Michael W. Hero,  

 

期刊: Bulletin of the London Mathematical Society  （WILEY Available online 2016）
卷期: Volume 25, issue 2  

页码: 157-161

 

ISSN:0024-6093

 

年代: 2016

 

DOI:10.1112/blms/25.2.157

 

出版商: Oxford University Press

 

数据来源: WILEY

 

摘要:

Letfbe a continuous self‐map of the unit circle,S1. The ω‐limit points ω(x) of a pointxare the set of all limit points of the sequence of iterates offacting onx. We shall show that the set of all ω‐limit points∪x∈s1ω(x)is a closed set inS1.

 

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