My question is about the closure of the periodic point for the logistic family $f_\lambda(x) = \lambda x(1-x)$ of maps of the interval $[0,1]$.

Is there an explicit parameter $\lambda$ for which the set of periodic points is not dense in the nonwandering set of the map $f_\lambda$?

Lai San Young showed in 1979that the periodic points are dense in the closure of the recurrent points. Nitecki gave an example of an unimodal map for which the periodic points are not dense in the nonwandering set. Universality of the logistic family should imply the existence of such a parameter .