03/01/2012, 12:09 AM
(This post was last modified: 03/01/2012, 12:10 AM by sheldonison.)

(02/29/2012, 11:49 PM)Kouznetsov Wrote: 1. Are the multiple cut lines unavoidable?Hey Dimitrii, the multiple cut points arises when the base is inside the Shell Thron region, because one of the two fixed points is an attracting fixed point. Such an attracting fixed point is periodic, with multiple instances of sexp(z)=0, sexp(z-1)=singularity.

Can you define the superexponential with only one cut line from the point -2 for each base?

I would like to declare such superexponential as the "true and only" tetration.

2. I cite your article at http://tori.ils.uec.ac.jp/TORI/index.php...mplex_base

If the base is outside the Shell Thron region, then both of the fixed points are repelling, and then there is only one singularity cut point in the graph, and that singularity is at z=-2. This is the case for the 2nd of the four graphs I posted, b=2+0.51i. But the first graph, case, which is nearby, with b=2+0.56i, but inside the Shell Thron boundary, has iterated singularities based on the period of the upper fixed point.

- Sheldon