04/25/2010, 08:22 AM
Another one:
\( f(x)=x^2+(1+\sqrt{5})x+1 \)
\( F(x)=e^{2^x} - \frac{1+\sqrt{5}}{2} \)
\( f \) has two fixed points with the derivations:
\( f'(\frac{1-\sqrt{5}}{2}) = 2 \) and
\( f'(\frac{-1-\sqrt{5}}{2}) = 0 \).
The above superfunction \( F \) is the regular iteration at the upper fixed point \( \frac{1-\sqrt{5}}{2} \)
\( f(x)=x^2+(1+\sqrt{5})x+1 \)
\( F(x)=e^{2^x} - \frac{1+\sqrt{5}}{2} \)
\( f \) has two fixed points with the derivations:
\( f'(\frac{1-\sqrt{5}}{2}) = 2 \) and
\( f'(\frac{-1-\sqrt{5}}{2}) = 0 \).
The above superfunction \( F \) is the regular iteration at the upper fixed point \( \frac{1-\sqrt{5}}{2} \)