Thread Rating:
  • 1 Vote(s) - 3 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Functional super-iteration and hierarchy of functional hyper-iterations
(05/02/2009, 06:14 PM)Tetratophile Wrote: A function might have no fixed points, and superiterations of a function may not even be continuous. I just wanna know what areas of mathematics do they use when doing real-valued iteraitons?

But before, one should really look at integer functions where your definition is unambigous. I am not especially aware that someone defined/used such a construct. If so I guess it belongs to recursion theory, like the Ackermann function.

But as Andrew mentioned: As soon we get a parabolic fixed point, this fixed point stays forever. That means you can do regular iteration there and have even an analytic hierarchy.

Messages In This Thread
RE: Functional super-iteration and hierarchy of functional composition-based operations - by bo198214 - 05/02/2009, 07:27 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Thoughts on hyper-operations of rational but non-integer orders? VSO 2 153 09/09/2019, 10:38 PM
Last Post: tommy1729
  [MSE] Shape of orbit of iterations with base b on Shell-Thron-region Gottfried 3 352 08/18/2019, 02:22 PM
Last Post: sheldonison
  Is bugs or features for super-logarithm? Ember Edison 10 1,144 08/07/2019, 02:44 AM
Last Post: Ember Edison
  A fundamental flaw of an operator who's super operator is addition JmsNxn 4 6,201 06/23/2019, 08:19 PM
Last Post: Chenjesu
  Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 1,601 06/10/2019, 04:29 AM
Last Post: Ember Edison
  Inverse super-composition Xorter 11 11,432 05/26/2018, 12:00 AM
Last Post: Xorter
  Math overflow question on fractional exponential iterations sheldonison 4 3,075 04/01/2018, 03:09 AM
Last Post: JmsNxn
  The super 0th root and a new rule of tetration? Xorter 4 3,309 11/29/2017, 11:53 AM
Last Post: Xorter
  Hyper-volume by integration Xorter 0 1,223 04/08/2017, 01:52 PM
Last Post: Xorter
  Functional power Xorter 0 1,148 03/11/2017, 10:22 AM
Last Post: Xorter

Users browsing this thread: 1 Guest(s)