Exploring the Tent-Map: Fixed Points & Stability

[squenshl]

Homework Statement

The "tent-map" is given by: x_n+1 = g(x_n) where g(x) = 2x if 0 <= x<= 1/2 and g(x) = 2-2x if 1/2 < x <= 1
a) Find the fixed points and their stability. Draw a cobweb plot of the tent map to demonstrate that your stability calculations are correct.
b) Find a period-2 orbit, and compute its stability.
c) It can be shown that the tent-map has period-n orbits for all n $\in$ N. Without doing any calculations explain why all of these periodic orbits must be unstable.

Homework Equations

The Attempt at a Solution

Done a). Got x = 0 and x = 2/3, both unstable and this is shown in the cobweb plot.
For b) I do x_n+2 = x_n and got 4 period-2 points, x = 0, x = 2/3, x = 4/7, x = 2/7, but I don't think these are right and how do you compute stability for these.
For c) Not too sure what they are asking here, it's not som obvious to me.
Any help on b) and c) would be great.

 

[micromass]

Your period 2 points are correct.
Now, how did you define stability for such a points?

 

[squenshl]

Is it just the same in as in part a)?

 

[squenshl]

I now get x = 0, 2/3, 2/5 and 4/5 as my period-2 orbits.