Thread Rating:
  • 1 Vote(s) - 5 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Universal uniqueness criterion?
#49
(07/04/2009, 11:17 PM)Tetratophile Wrote: *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?
The region G where the tetrtion is biholomorphic is plotted in figure 2 of
http://www.ils.uec.ac.jp/~dima/PAPERS/2009uniabel.pdf
exp(G) is shown at the right (between green and blue curves) and
log(G) is shown at the legt (between the red curve and the black line).
One has no need to evaluate tetration in order to plot this figure.
The region G is filled with lines of constant real part of arctetration and lines of constant imaginary part in figure 1b of
http://www.ils.uec.ac.jp/~dima/PAPERS/2009fractae.pdf
You may extract the figures mentioned and just overlap them.
Reply


Messages In This Thread
Universal uniqueness criterion? - by bo198214 - 05/21/2008, 06:24 PM
RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 05:19 AM
RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 06:42 AM
RE: Universal uniqueness criterion? - by bo198214 - 05/22/2008, 11:25 AM
RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 03:11 PM
RE: Universal uniqueness criterion? - by bo198214 - 05/22/2008, 05:55 PM
RE: Universal uniqueness criterion? - by bo198214 - 05/23/2008, 12:07 PM
Uniqueness of analytic tetration - by Kouznetsov - 09/30/2008, 07:58 AM
RE: Universal uniqueness criterion? - by bo198214 - 10/04/2008, 11:19 PM
RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 02:51 PM
RE: miner error found in paper - by bo198214 - 06/19/2009, 04:53 PM
RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 06:25 PM
RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 07:59 PM
RE: Universal uniqueness criterion? - by bo198214 - 06/20/2009, 02:10 PM
RE: Universal uniqueness criterion? - by Kouznetsov - 07/05/2009, 08:28 AM
RE: Universal uniqueness criterion? - by bo198214 - 07/05/2009, 06:54 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Semi-exp and the geometric derivative. A criterion. tommy1729 0 1,184 09/19/2017, 09:45 PM
Last Post: tommy1729
  A conjectured uniqueness criteria for analytic tetration Vladimir Reshetnikov 13 10,308 02/17/2017, 05:21 AM
Last Post: JmsNxn
  Uniqueness of half-iterate of exp(x) ? tommy1729 14 13,902 01/09/2017, 02:41 AM
Last Post: Gottfried
  Removing the branch points in the base: a uniqueness condition? fivexthethird 0 1,440 03/19/2016, 10:44 AM
Last Post: fivexthethird
  [2014] Uniqueness of periodic superfunction tommy1729 0 1,815 11/09/2014, 10:20 PM
Last Post: tommy1729
  Real-analytic tetration uniqueness criterion? mike3 25 19,871 06/15/2014, 10:17 PM
Last Post: tommy1729
  exp^[1/2](x) uniqueness from 2sinh ? tommy1729 1 2,105 06/03/2014, 09:58 PM
Last Post: tommy1729
  Uniqueness Criterion for Tetration jaydfox 9 10,691 05/01/2014, 10:21 PM
Last Post: tommy1729
  Uniqueness of Ansus' extended sum superfunction bo198214 4 6,363 10/25/2013, 11:27 PM
Last Post: tommy1729
  A question concerning uniqueness JmsNxn 3 5,308 10/06/2011, 04:32 AM
Last Post: sheldonison



Users browsing this thread: 1 Guest(s)