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

DOI:
https://doi.org/10.1090/S0002-9939-1984-0760951-6

MathSciNet review:
760951

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1984-0760951-6

Article copyright:
© Copyright 1984
American Mathematical Society