Talk:Iterated function
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Function Iteration was redirected to Function composition. Should this article redirect there as well (after any necessary merging)? - dcljr (talk) 18:58, 11 November 2005 (UTC)
Merge with Recurrence relation?
It appears that the articles Recurrence relation and Iterated function are about the same thing. Is there any objection to merging them? Which should be merged into which? Duoduoduo (talk) 22:52, 28 May 2010 (UTC)
See discussion at talk:Recurrence relation. —Preceding unsigned comment added by Jowa fan (talk • contribs) 06:19, 1 June 2010 (UTC)
Someone can help?
Surely the expressions can be by far non rigurous, but can be someone to look my notes on [1] and improve that or comment about? — Preceding unsigned comment added by 80.25.164.213 (talk) 20:06, 20 July 2012 (UTC)
- I sense you are in the wrong article, except perhaps for the brief summary remarks of the "Conjugacy" section. You are replicating, in somewhat idiosyncratic language, the continuous iteration orbit theory of Schröder's equation. Possibly Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1088/1751-8113/44/40/405205, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with
|doi=10.1088/1751-8113/44/40/405205instead. is useful. Cuzkatzimhut (talk) 20:16, 20 July 2012 (UTC)
My little contribution
From my time as student I develop some aproximation to this field. Maybe some ideas can be useful. [2] — Preceding unsigned comment added by 80.25.164.213 (talk) 10:27, 20 August 2012 (UTC)
- Your compositional index eqn is Abel's equation, with a standardized theory: You are constructing Koenigs function for Schröder's equation.Cuzkatzimhut (talk) 10:56, 20 August 2012 (UTC)
Existence and uniqueness of fractional and continuous iterates
I think the article should say a bit more about the question of existence and uniqueness (or lack thereof) of fractional and continuous iterates. At the moment it simply says "In some instances, fractional iteration of a function can be defined", which is not tremendously illuminating. 86.160.216.252 (talk) 13:31, 24 October 2012 (UTC)
- My own sense is that this article here is a popular entryway into the subject, and anyone more seriously interested and more mathematically inclined to worry about existence and uniqueness would have moved on to Schröder's equation and thence Koenigs function, where such issues belong, a while ago — if not Böttcher's equation and Abel's equation. I assume the reader of this article is an engineer or an undergraduate, the reader of Schröder's equation a graduate student, and that of Koenigs function, a mathematically sophisticated reader. If one wished to adduce the first Kuczma book reference after "defined", that might useful. But adducing the Szekeres, etc... references that address the problem properly and completely would be overkill, and could only alienate the "first contact" reader seeking something compact and practical....Cuzkatzimhut (talk) 15:03, 24 October 2012 (UTC)
- I agree that this article should not go into enormous technical detail about this topic. I just think it should say a bit more than it presently does about the two questions "Do fractional/continous iterations always exist (e.g. for "sensible" continuous functions)?" and "If they exist, are they unique?". It only needs to be a handful of lines, with perhaps a couple of examples. I think this is of general interest to the curious reader. 86.160.216.252 (talk) 17:15, 24 October 2012 (UTC)
- Indeed, a few evocative illustrations might be helpful, if simple. Cuzkatzimhut (talk) 18:27, 24 October 2012 (UTC)
- I agree that this article should not go into enormous technical detail about this topic. I just think it should say a bit more than it presently does about the two questions "Do fractional/continous iterations always exist (e.g. for "sensible" continuous functions)?" and "If they exist, are they unique?". It only needs to be a handful of lines, with perhaps a couple of examples. I think this is of general interest to the curious reader. 86.160.216.252 (talk) 17:15, 24 October 2012 (UTC)
f k notation
There was a section in inverse function related to f 2, f k, and so, that I trimmed due to obvious WP:stay on topic concerns. Can somebody reuse this stuff here? Incnis Mrsi (talk) 15:35, 3 July 2013 (UTC)
Verifying some formulas for fractional iteration
The section Some formulas for fractional iteration is very similar to my own unpublished results. My question is, can anyone verify the formulas are in a peer reviewed published work? Daniel Geisler (talk) 20:21, 13 May 2014 (UTC)
- My notes too, of course. Please sign your posts. You are referring to the off-the-bat power series expansion around a fixed point that, I trust, you saw in the History of the article, User:Drschawrz adduced in August 2011? This is the frontal--and inefficient--assault to the problem, that, mercifully, Schroeder has provided the more systematic solution to a century and a half ago. Try reproducing his results on the table of section 9 (Examples) that way! Conjugacy is of course the way to go. Most standard courses on iterated functions and textbooks have, naturally, one version of them or another. You are unhappy with the Carleson and Gamelin 1993 text? Cuzkatzimhut (talk) 00:22, 14 May 2014 (UTC)
- The issue is whether the Taylors series can be validated by a peer reviewed article in a published journal. Am I unhappy with the Carleson and Gamelin 1993 text? Actually I contacted one of the authors and he said he no longer worked with complex dynamics. My concern is that while the Classification of Fixed Points documents the Schroeder and Abel equations, it does it in a round about way and provides no explanation of why they are necessary. The power series expansion around a fixed point has interesting combinatorial properties besides providing a natural explanation for both the Schroeder and Abel equations. Daniel Geisler (talk) 06:54, 14 May 2014 (UTC)
- You are evidently proposing rewrites of the Carleman matrix algorithm, which most of the references cited here hew to. An ambitious project. The Scroeder equation solves the project for somebody more advanced than the novice coming to this specific article here, as discussed above. Further technicalities would only obscure the picture here---but you could test-drive your proposals on superfunction which needs your, and anyone's really!, help. Are you sure you contacted the author User:Drschawrz of these sections? Cuzkatzimhut (talk) 10:44, 14 May 2014 (UTC)
- The issue is whether the Taylors series can be validated by a peer reviewed article in a published journal. Am I unhappy with the Carleson and Gamelin 1993 text? Actually I contacted one of the authors and he said he no longer worked with complex dynamics. My concern is that while the Classification of Fixed Points documents the Schroeder and Abel equations, it does it in a round about way and provides no explanation of why they are necessary. The power series expansion around a fixed point has interesting combinatorial properties besides providing a natural explanation for both the Schroeder and Abel equations. Daniel Geisler (talk) 06:54, 14 May 2014 (UTC)
It's been a week and nobody has provided any reason to think that the section on fractional iteration can be validated through being published. Ironically I don't disagree with the results, I just think they should be published first. Daniel Geisler (talk) 11:22, 21 May 2014 (UTC)
- ? What exactly is your point? You are proposing to delete section 6 until somebody finds a remote refereed attribution for the elementary examples? As I indicated, this would be detrimental to the article, but not a tragedy, as they are misleading in suggesting to the reader how professionals in the field actually solve such equations in practice. To me, the examples appear obvious--the first naive thing that crosses one's mind--albeit off the mark. Starting from Babbage and continuing with Schroeder, both in the 19th century, conjugacy is the answer. Check it out on the iteration orbit of, e.g. sin(x) as contrasted to the actual answer, e.g. in [the roots of sine]. However, at the end of the day, I see no actual harm in these examples. Cuzkatzimhut (talk) 12:59, 21 May 2014 (UTC)
Should this page be renamed to "Function iteration"?
I've rewritten the lead to make it make sense at least marginally. However, it struck me that the article seems to be more about the general notion of iterating functions (as a generaly activity, or subject of study) than about the specific subject of functions that are of the form f n. Therefore I think the name "Function iteration" would much better cover the contents than "Iterated function". Marc van Leeuwen (talk) 08:42, 18 February 2015 (UTC)