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

 

A counterexample in dynamical systems of the interval


Authors: Hsin Chu and Jin Cheng Xiong
Journal: Proc. Amer. Math. Soc. 97 (1986), 361-366
MSC: Primary 58F20; Secondary 58F08
MathSciNet review: 835899
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Abstract: In [1] it was proved that if the recurrent points of a continuous map of the unit interval form a closed set, then this map has no periodic point with period not equal to a power of 2, i.e. this map is of type $ {2^\infty }$. In this paper we will construct a continuous map of the interval which is of type $ {2^\infty }$ and for which the set of recurrent points is not closed. By such a counterexample it may be shown that some of the results announced in [2] are not correct.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0835899-0
PII: S 0002-9939(1986)0835899-0
Keywords: Recurrent point, periodic point, type $ {2^\infty }$
Article copyright: © Copyright 1986 American Mathematical Society