A counterexample in dynamical systems of the interval

Chu, Hsin; Xiong, Jin Cheng

doi:10.1090/S0002-9939-1986-0835899-0

A counterexample in dynamical systems of the interval
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by Hsin Chu and Jin Cheng Xiong PDF

Proc. Amer. Math. Soc. 97 (1986), 361-366 Request permission

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.

References

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The asymptotic behaviour of one-dimensional dynamical systems

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