The location of the period two orbit is found from equation (2.11),
and
These two points belong to the period two orbit. We label
the left point 
and the right point 
.
Note that the location of the period two orbit produces complex
numbers for 
. This indicates that the period two orbit exists
only for 
, which is obvious
geometrically since 
begins a new intersection with the straight
line y = x at 
.
The stability of this period two orbit is determined by rewriting equation (2.13) as
where we used equations (2.19) and (2.20) for and .
A plot of
the stability for the period two orbit is presented in Figure 2.12.
Figure 2.12: Stability of period two orbit.
A close examination of this
figure shows that, for 
, the absolute value of the stability
function is less than one; that is, the period two orbit is stable. For
, the period two orbit is unstable.
The range in 
for which the period two orbit is stable can actually be
obtained analytically. The period two orbit is
stable as long as
The period two orbit first becomes stable when 
which occurs
at , and it loses stability at 
which the reader
can verify takes place at 
(see Prob. 2.17).
