10/06/2007, 07:05 AM
Here the promised graph of the difference of the (regular) iterational square root taken at the fixed point 2 and taken at the fixed point 4 of \( \sqrt{2}^x \). Unfortunately 150 digits took too long, instead I now computed it with at least 50 digits precision (which took more then 7 hours).
I think this pattern will show up for every analytic function with two neighbored fixed point. The question still remains to find an analytic function \( \neq \text{id} \) where the difference is 0.
I think this pattern will show up for every analytic function with two neighbored fixed point. The question still remains to find an analytic function \( \neq \text{id} \) where the difference is 0.