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.

Please help.

Katy