The power law map has a variation |x-0.5|1+b near x=0.5. For 0<b<1 the derivative of the curve is zero at x=0.5, so the curve still has a maximum, but is non analytic here. First we look at the map itself and the iterations, e.g. for b=0.5, a=2.6
Now look at the sequence of bifurcations for 1.93<a<2.33:
and the Lyapunov curve
The qualitative appearance is quite similar to the quadratic and sine maps, with a sequence of period doubling bifurcations accumulating at around a=2.3. However following the same procedure as before you can show that the values of and are in fact different than for the two examples of a quadratic maximum.Return to text.