question about regular iteration, also about tetration properties in general
#2
(05/03/2009, 02:49 AM)Tetratophile Wrote: Could anyone tell me what "regular iteration" means? just generally, not for any specivic method.

Its regular if the iterates are differentiable (or at leas asymptotically differentiable) at the fixed point. This implies that \( (f^{[t]})'(x_0) = f'(x_0)^t \).

Perhaps you have tried that already yourself: If you try graphically find the half iterate you start at a certain interval and then continue to the right and to the left. Depending how you choose the function on the initial segment, the function gets more wobbly or more smooth. Without a fixed point I dont know a criterion of the most unwobbly function, however at the fixed point you can express this unwobblyness by being differentiable.

For the wobblyness of a function without fixed point see the pictures made by Gottfried in the thread another uniqueness musing.


Messages In This Thread
RE: question about regular iteration - by bo198214 - 05/03/2009, 07:05 AM

Possibly Related Threads…
Thread Author Replies Views Last Post
  Question about the properties of iterated functions Shanghai46 9 2,239 04/21/2023, 09:07 PM
Last Post: Shanghai46
  Matrix question for Gottfried Daniel 6 2,225 12/10/2022, 09:33 PM
Last Post: MphLee
  What are the types of complex iteration and tetration? Daniel 5 2,224 08/17/2022, 02:40 AM
Last Post: JmsNxn
  [question] Local to global and superfunctions MphLee 8 2,719 07/17/2022, 06:46 AM
Last Post: JmsNxn
Question Natural Properties of the Tetra-Euler Number Catullus 6 2,526 07/01/2022, 08:16 AM
Last Post: Catullus
  A random question for mathematicians regarding i and the Fibonacci sequence. robo37 1 4,934 06/27/2022, 12:06 AM
Last Post: Catullus
  Question about tetration methods Daniel 17 6,283 06/22/2022, 11:27 PM
Last Post: tommy1729
  Fractional iteration of x^2+1 at infinity and fractional iteration of exp bo198214 17 36,399 06/11/2022, 12:24 PM
Last Post: tommy1729
  A question concerning uniqueness JmsNxn 4 11,667 06/10/2022, 08:45 AM
Last Post: Catullus
  Categories of Tetration and Iteration andydude 13 34,679 04/28/2022, 09:14 AM
Last Post: MphLee



Users browsing this thread: 1 Guest(s)