Real tetration as a limit of complex tetration

[tommy1729]

I agree with Daniel.

I had similar ideas in the past.
I made a post somewhere I am sure of that.


The thing is this :

If the derivative at the fixpoint has small imaginary value the angular rotation is small.

So if the fixpoint is also far away , combined with bounded angular rotation , we get almost no rotation.

The rotation converges to zero if the distance to the fixpoint converges to infinity and we pick a subset that has small angular rotation ( aka imag part of the derivative ).

So the question is ; is it justified to take that limit ?? 

Does that converge properly to a unique and analytic function ?

I am not sure any of this or a variant is even justified but it is worth investigating.



regards

tommy1729