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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Isolated chain recurrent points for one-dimensional maps


Authors: Louis Block and John E. Franke
Journal: Proc. Amer. Math. Soc. 94 (1985), 728-730
MSC: Primary 58F08; Secondary 54H20, 58F20
DOI: https://doi.org/10.1090/S0002-9939-1985-0792292-6
MathSciNet review: 792292
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Abstract: For a continuous map of the interval to itself or of the circle to itself, we show that any isolated chain recurrent point is eventually periodic. Furthermore, an isolated chain recurrent point which is not in the orbit of a critical point and has no critical point in its orbit is periodic.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0792292-6
Article copyright: © Copyright 1985 American Mathematical Society