Hi, I have this problem.
I need to sketch a bifurcation diagram for the fixed points of the family where .
I have that the fixed points are and
I know that:
When drops below the identity mapping and so there is only one fixed point at
When the identity mapping is tangent to and so there are 2 fixed points at and
When rises above the identity mapping and so there are 3 one fixed points at x=0 and
So i can sort of picture how the diagram will look, I just can't figure out for what values of the fixed points will be repelling/attracting.
I know that at the last two fixed points. And that if then fixed point is an attractor and if then fixed point is a repellor. But i'm stuck here.