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
  Iteration with two analytic fixed points bo198214 42 498 08/12/2022, 11:28 PM
Last Post: JmsNxn
  Qs on extension of continuous iterations from analytic functs to non-analytic Leo.W 17 811 08/10/2022, 11:34 PM
Last Post: JmsNxn
  Apropos "fix"point: are the fractional iterations from there "fix" as well? Gottfried 12 550 07/19/2022, 03:18 AM
Last Post: JmsNxn
  [note dump] Iterations and Actions MphLee 23 3,490 07/15/2022, 04:08 PM
Last Post: MphLee
  Constructing an analytic repelling Abel function JmsNxn 0 105 07/11/2022, 10:30 PM
Last Post: JmsNxn
  Is tetration analytic? Daniel 6 249 07/08/2022, 01:31 AM
Last Post: JmsNxn
  Consistency in the composition of iterations Daniel 9 473 06/08/2022, 05:02 AM
Last Post: JmsNxn
  Has anyone solved iterations of z+Γ(z)? Leo.W 5 2,061 01/07/2022, 08:15 AM
Last Post: JmsNxn
  On the [tex]2 \pi i[/tex]-periodic solution to tetration, base e JmsNxn 0 674 09/28/2021, 05:44 AM
Last Post: JmsNxn
  A compilation of graphs for the periodic real valued tetrations JmsNxn 1 920 09/09/2021, 04:37 AM
Last Post: JmsNxn



Users browsing this thread: 1 Guest(s)