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.
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