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


Messages In This Thread
Periodic analytic iterations by Riemann mapping - by tommy1729 - 03/02/2016, 01:26 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  [MSE] Shape of orbit of iterations with base b on Shell-Thron-region Gottfried 14 3,607 12/13/2019, 02:33 PM
Last Post: Ember Edison
  Half-iterates and periodic stuff , my mod method [2019] tommy1729 0 480 09/09/2019, 10:55 PM
Last Post: tommy1729
  Math overflow question on fractional exponential iterations sheldonison 4 4,068 04/01/2018, 03:09 AM
Last Post: JmsNxn
  [repost] A nowhere analytic infinite sum for tetration. tommy1729 0 1,297 03/20/2018, 12:16 AM
Last Post: tommy1729
Question Analytic matrices and the base units Xorter 2 2,588 07/19/2017, 10:34 AM
Last Post: Xorter
  Non-analytic Xorter 0 1,514 04/04/2017, 10:38 PM
Last Post: Xorter
  A conjectured uniqueness criteria for analytic tetration Vladimir Reshetnikov 13 11,975 02/17/2017, 05:21 AM
Last Post: JmsNxn
  Is bounded tetration is analytic in the base argument? JmsNxn 0 1,452 01/02/2017, 06:38 AM
Last Post: JmsNxn
  Are tetrations fixed points analytic? JmsNxn 2 3,161 12/14/2016, 08:50 PM
Last Post: JmsNxn
  The bounded analytic semiHyper-operators JmsNxn 2 3,818 05/27/2016, 04:03 AM
Last Post: JmsNxn



Users browsing this thread: 1 Guest(s)