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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The chain recurrent set for maps of the circle


Authors: Louis Block and John E. Franke
Journal: Proc. Amer. Math. Soc. 92 (1984), 597-603
MSC: Primary 58F12; Secondary 54H20, 58F20
MathSciNet review: 760951
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Abstract: For a continuous map of the circle to itself we give necessary and sufficient conditions for the chain recurrent set to be precisely the set of periodic points. We also examine the possible types of examples which can occur, where the set of periodic points is closed and nonempty, but there are nonperiodic, chain recurrent points.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0760951-6
PII: S 0002-9939(1984)0760951-6
Article copyright: © Copyright 1984 American Mathematical Society