Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
fractional iterates of arg(z) and |z|
#1
Is it possible to define a function
h(h(z)) = |z|, h(z) =/= |z|

or
h(h(z)) = arg(z)

I wonder because these seem like difficult functions to crack, considering they have no Taylor series.
Reply
#2
(03/31/2011, 08:28 PM)JmsNxn Wrote: Is it possible to define a function
h(h(z)) = |z|, h(z) =/= |z|

or
h(h(z)) = arg(z)

I wonder because these seem like difficult functions to crack, considering they have no Taylor series.

We could set h(z) = |z| for z with non-negative real part, h(z) = -iz for z with negative real and non-negative imaginary part, and h(z) = iz for z with negative and imaginary parts. Then we'd get h(h(z)) = |z| for all z. A similar technique should work for h(h(z)) = arg(z).
Reply
#3
Tongue that was easy
Reply


Possibly Related Threads...
Thread Author Replies Views Last Post
  Merged fixpoints of 2 iterates ? Asymptotic ? [2019] tommy1729 1 77 09/10/2019, 11:28 AM
Last Post: sheldonison
  Half-iterates and periodic stuff , my mod method [2019] tommy1729 0 37 09/09/2019, 10:55 PM
Last Post: tommy1729
  Approximation to half-iterate by high indexed natural iterates (base on ShlThrb) Gottfried 1 139 09/09/2019, 10:50 PM
Last Post: tommy1729
  Math overflow question on fractional exponential iterations sheldonison 4 2,986 04/01/2018, 03:09 AM
Last Post: JmsNxn
  [MSE] Fixed point and fractional iteration of a map MphLee 0 1,909 01/08/2015, 03:02 PM
Last Post: MphLee
  Fractional calculus and tetration JmsNxn 5 6,612 11/20/2014, 11:16 PM
Last Post: JmsNxn
  Theorem in fractional calculus needed for hyperoperators JmsNxn 5 5,985 07/07/2014, 06:47 PM
Last Post: MphLee
  Further observations on fractional calc solution to tetration JmsNxn 13 12,778 06/05/2014, 08:54 PM
Last Post: tommy1729
  Negative, Fractional, and Complex Hyperoperations KingDevyn 2 5,732 05/30/2014, 08:19 AM
Last Post: MphLee
  left-right iteraton in right-divisible magmas, and fractional ranks. MphLee 1 2,603 05/14/2014, 03:51 PM
Last Post: MphLee



Users browsing this thread: 1 Guest(s)