Thread Rating:
  • 1 Vote(s) - 5 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Periodic analytic iterations by Riemann mapping
#1
Let r denote riemann mapping.
r' denotes the functional inverse of r.

Let j be An analytic jordan curve around the origin.

R maps j to the unit circle.

Let r'(1) be the starting point A.

then iterations f^[x](r'(1)) with x > 0 ( real ) are periodic and analytic iff

F(z) = r' ( T ( r) ).
Where T is a complex number on the unit circle.

I think this is correct.

This seems to suggest exp has no periodIC iterational Jordan curve away from its fixpoints.

Regards

Tommy1729

Reply
#2
Strongly related

http://math.eretrandre.org/tetrationforu...p?tid=1038

Regards

Tommy1729
Reply


Possibly Related Threads...
Thread Author Replies Views Last Post
  Has anyone solved iterations of z+Γ(z)? Leo.W 3 130 10/03/2021, 09:17 PM
Last Post: tommy1729
  On the [tex]2 \pi i[/tex]-periodic solution to tetration, base e JmsNxn 0 92 09/28/2021, 05:44 AM
Last Post: JmsNxn
  A compilation of graphs for the periodic real valued tetrations JmsNxn 1 273 09/09/2021, 04:37 AM
Last Post: JmsNxn
  Brute force tetration A_k(s) is analytic ! tommy1729 9 2,080 03/22/2021, 11:39 PM
Last Post: JmsNxn
  Nixon-Banach-Lambert-Raes tetration is analytic , simple and “ closed form “ !! tommy1729 11 3,339 02/04/2021, 03:47 AM
Last Post: JmsNxn
  [MSE] Shape of orbit of iterations with base b on Shell-Thron-region Gottfried 14 16,927 12/13/2019, 02:33 PM
Last Post: Ember Edison
  Half-iterates and periodic stuff , my mod method [2019] tommy1729 0 1,996 09/09/2019, 10:55 PM
Last Post: tommy1729
  Math overflow question on fractional exponential iterations sheldonison 4 8,791 04/01/2018, 03:09 AM
Last Post: JmsNxn
  [repost] A nowhere analytic infinite sum for tetration. tommy1729 0 2,843 03/20/2018, 12:16 AM
Last Post: tommy1729
Question Analytic matrices and the base units Xorter 2 5,127 07/19/2017, 10:34 AM
Last Post: Xorter



Users browsing this thread: 1 Guest(s)