A Special Parameter Value for the Logistic Map

This Demonstration considers the iterations of the logistic map for . The Demonstration "An Interval Eventually Bounding Trajectories of the Logistic Map" showed how every trajectory with a starting point in (0, 1) is eventually contained in .

This Demonstration shows that there cannot be any odd periodic orbit if . In fact, in that case the interval is mapped into the interval and is mapped into . It is also easy to show that the points and do not lead to an odd periodic orbit. The previous statements are not true if .

It is possible to limit by , as it is well known that for there is no periodic orbit.