I have $z\mapsto 1-1/z^2$ which has the periodic orbit {$1,0,\infty$} on the Riemann sphere. Next, I want to calculate the corresponding multiplier \lambda= (f^{\circ n})' (z_i)=f'(z_1)\cdots f'(z_n). In this example we have f'(z)=2/z^3, hence \lambda=f'(1) f'(0) f'(\infty)=2/1 \cdot 2/0 \cdot 2/\infty =\, ???.
What is wrong here? (I shall prove that $\lambda=0$).
Thanks for your help!