07/04/2009, 11:17 PM
(This post was last modified: 07/04/2009, 11:39 PM by Base-Acid Tetration.)
"bo198214 Wrote:2. may hit , i.e. the extension of overlaps with the original domain. If meets at an angle then meets at an angle . So the image curves rotate around L. This includes also the comment of Ben, that if , i.e. if is real, then then the images do not rotate, and hence one would never reach if it hits in a different angle.
*Fortunately the derivatives at the fixed points L and L* is not a real number, (they are 0.318...+1.337...i) Of course I'm talking about the fixed points of the principal branch of the logarithm.
*What is the problem with the extension overlapping with the original domain?
*What initial regions do all of the known methods of complex extensions of tetrations have? If their initial regions don't deviate too much from each other that their exponentials leave the domain of biholomorphy, we can prove the weaker theorem that all of the known extensions are the same. Can anyone show the (mapping graphs on the complex plane) exponentials and the logarithms of the intiial regions?