I am trying to find the periodic points for $x^3-x$ and find out whether or not they are repelling or attracting. I have been trying to use orbit diagrams to figure this out.
I know there are three fixed points $0,\sqrt{2}, -\sqrt{2}$
I can use the orbit diagram to find if are repelling or attracting. (I believe they are 0 is attracting and the other two are repelling)
But I am unsure how to tell if there are other periodic points.
I am also having trouble finding their stable set. I believe for the fixed points there is nothing in their stable set except for themselves. Since the spiral at 0 will only reach 0 at the value of 0