Thread Rating:
  • 1 Vote(s) - 5 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Inverse super-composition
#8
(12/25/2016, 04:38 PM)Xorter Wrote:
(12/25/2016, 04:16 AM)sheldonison Wrote: Your question is too general, since you don't identify what f(x) you are interested in. In general, the type of solution depends on the behavior at the fixed point. I assume you are interested in real valued functions. Some iterated functions have an attracting point. Then we look at the slope at the fixed point.

Yes, my question is general, because I am looking for a totally general solution for all the kind of problem like this.
Anyway, I found a nicer formula for my question instead of steinix-ankh, like this:

According to the knowledge of f and g, what is N? How can I calculate it?
For example:

Thus N must be = log2(x), but here is the question why and how can I know it from?

For a fixed point of zero, with a fixed point multiplier of 2, the general solution for the Abel function generated at the fixed point of zero is:


This is the Abel function for f(z)

where S(z) is the formal Schröder equation solution;

This is sometimes called Koenig's solution. It can be modified to work with any fixed point multiplier of k, |k|<>1. Using pari-gp one can easily write a program to generate the formal power series for S(x) given f(x).
- Sheldon
Reply


Messages In This Thread
Inverse super-composition - by Xorter - 11/24/2016, 12:53 PM
RE: Inverse super-composition - by JmsNxn - 11/25/2016, 08:55 PM
RE: Inverse super-composition - by Xorter - 12/23/2016, 01:33 PM
RE: Inverse super-composition - by JmsNxn - 12/23/2016, 08:12 PM
RE: Inverse super-composition - by Xorter - 12/24/2016, 09:53 PM
RE: Inverse super-composition - by sheldonison - 12/25/2016, 04:16 AM
RE: Inverse super-composition - by Xorter - 12/25/2016, 04:38 PM
RE: Inverse super-composition - by sheldonison - 12/25/2016, 08:35 PM
RE: Inverse super-composition - by Xorter - 12/25/2016, 10:23 PM
RE: Inverse super-composition - by sheldonison - 12/26/2016, 07:10 AM
RE: Inverse super-composition - by Xorter - 01/12/2017, 04:19 PM
RE: Inverse super-composition - by Xorter - 05/26/2018, 12:00 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Is bugs or features for fatou.gp super-logarithm? Ember Edison 10 1,648 08/07/2019, 02:44 AM
Last Post: Ember Edison
  A fundamental flaw of an operator who's super operator is addition JmsNxn 4 6,464 06/23/2019, 08:19 PM
Last Post: Chenjesu
  Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 2,148 06/10/2019, 04:29 AM
Last Post: Ember Edison
  Inverse Iteration Xorter 3 2,108 02/05/2019, 09:58 AM
Last Post: MrFrety
  The super 0th root and a new rule of tetration? Xorter 4 3,493 11/29/2017, 11:53 AM
Last Post: Xorter
  the inverse ackerman functions JmsNxn 3 5,600 09/18/2016, 11:02 AM
Last Post: Xorter
  Uniterated composition Xorter 2 2,950 09/15/2016, 05:17 PM
Last Post: MphLee
  Solving tetration using differintegrals and super-roots JmsNxn 0 1,772 08/22/2016, 10:07 PM
Last Post: JmsNxn
  The super of exp(z)(z^2 + 1) + z. tommy1729 1 2,415 03/15/2016, 01:02 PM
Last Post: tommy1729
  Super-root 3 andydude 10 10,087 01/19/2016, 03:14 AM
Last Post: andydude



Users browsing this thread: 1 Guest(s)