Thread Rating:
  • 3 Vote(s) - 2.33 Average
  • 1
  • 2
  • 3
  • 4
  • 5
2 real fixpoints ... 3 iterations ?
#1
ok , first i dont know if this has been asked or answered before , so forgive my ignorance if such is the case.

consider an analytic function f(z) , strictly rising on the reals with 2 real fixpoints.

now we can use regular iteration for each fixpoint and thus get two ' zones ' that are ' correct ' half-iterates. ( assuming radius = oo too )

sketch :

[ - oo .. zone 1 .. fixpoint 1 .. zone 2 .. fixpoint 2 .. zone 3 .. + oo ]

when expanded at fixpoint 1 and missing the fixpoint 2 ( and radius oo ) i consider that regular half-iterate as a correct solution to 'zone 1'

similarly :

when expanded at fixpoint 2 and missing the fixpoint 1 ( and radius oo ) i consider that regular half-iterate as a correct solution to 'zone 3'


So the question becomes , what gives zone 2 ?


Regards

Tommy1729
Reply


Messages In This Thread
2 real fixpoints ... 3 iterations ? - by tommy1729 - 08/08/2009, 11:31 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Merged fixpoints of 2 iterates ? Asymptotic ? [2019] tommy1729 1 126 09/10/2019, 11:28 AM
Last Post: sheldonison
  [MSE] Shape of orbit of iterations with base b on Shell-Thron-region Gottfried 3 339 08/18/2019, 02:22 PM
Last Post: sheldonison
  Math overflow question on fractional exponential iterations sheldonison 4 3,061 04/01/2018, 03:09 AM
Last Post: JmsNxn
  b^b^x with base 0<b<e^-e have three real fixpoints Gottfried 1 2,009 11/07/2017, 11:06 AM
Last Post: sheldonison
  2 fixpoints , 1 period --> method of iteration series tommy1729 0 1,267 12/21/2016, 01:27 PM
Last Post: tommy1729
  2 fixpoints related by power ? tommy1729 0 1,270 12/07/2016, 01:29 PM
Last Post: tommy1729
  Periodic analytic iterations by Riemann mapping tommy1729 1 1,972 03/05/2016, 10:07 PM
Last Post: tommy1729
  2 real fixpoints again ....... tommy1729 10 8,159 02/23/2016, 10:17 PM
Last Post: tommy1729
  Fixpoints a,b with f ' (a) = f ' (b) = 1 tommy1729 0 1,478 09/15/2015, 08:29 AM
Last Post: tommy1729
  Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x Ivars 10 13,743 03/29/2015, 08:02 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)