Continuous iteration

[bo198214]

To quote thr Rolling Stones, "you can't always get what you want".

Not always, however in this case you can see on the basis of our discussions that we are quite close to "the" real solution. It even seems that this solution concides with the solution obtained from regular iteration at the fixed points for the basis \( b<e^{1/e} \). However lots of proofs are still lacking.

I think the first fixed point I used was attracting and the neighoring fixed point was repelling. In general the hyperbolic fixed points are repelling and are found using iterated logs with a given branch.

For each fixed point the conjugate is also a fixed point, I would imagine that such a pair yields the same solution, however different from the solutions obtained at other fixed point pairs.