02/25/2013, 01:42 AM
(This post was last modified: 02/25/2013, 01:08 PM by sheldonison.)
(02/24/2013, 08:57 PM)bo198214 Wrote:I have gotten results on the STB itself; although the calculation is indirect, and requires calculating complex tetration for many dozens of complex bases in a circle. See http://math.eretrandre.org/tetrationforu...e=threaded for the irrationally indifferent case and the next entry in that thread for the rationally indifferent case. I think the rationally indifferent case, with a "pseudo" period=5, base=1.96514 + 0.441243i, is a very interesting case, and I was hoping someone had calculated the analogous problem for Mandelbrots inverse perturbed-fatou coordinates on the main cardioid boundary, with a rational Pseudo period.(02/21/2013, 09:01 AM)sheldonison Wrote: We did see some results for bases both inside and outside the Shell Thron boundary.
Oh Sheldon, I am really too slow to catch up with all your findings. Indeed now that I plotted some sickles it seems to me the Shell/Thron boundary is not much of an osbtacle anymore. Whether this follows from the propositions of Shishikura is perhaps another matter.
So the general assumption in the moment is that we can continue tetration along bases through the STB?
Dimitrii's also reports that his Cauchy integral algorithm can calculate bases on the Shell Thron boundary directly. I have also extended my indirect results to z anywhere in the complex plane for bases on the STB.
Quote:What aboutitself, do we conjecture holomorphy there?
What happened anyway with writing your article. I really find that its a novel efficient way to compute tetration, worth that the world should know it!
I'll try to get to that article ... thanks for the encouragement. I still have much to learn.
- Sheldon