A counterexample in dynamical systems of the interval

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 ∞ {2^\infty } . In this paper we will construct a continuous map of the interval which is of type 2 ∞ {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.