Talk:Iterated function: Difference between revisions

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When the article says, "Note: these two special cases of ax2 + bx + c are the only cases that have a closed-form solution. Choosing b = 2 = –a and b = 4 = –a, respectively, further reduces them to the nonchaotic and chaotic logistic cases discussed prior to the table." Does it mean that we only know of two closed form solutions, or has it been proven that there are no others? <small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/75.243.141.93|75.243.141.93]] ([[User talk:75.243.141.93|talk]]) 21:20, 4 October 2015 (UTC)</small><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

:Well, a "proof" for the absence of a closed form solution might be hard to conceive, mostly because "closed form" is a bit of a subjective label: it is predicated on agreement of what the "closed form" solutions of [[Schröder's equation]] may include. You may see, though, in conventional language, from the original Schroeder paper of 1870 that they really ''have'' to be just these two for the [[logistic map]], and the Katsura and Fukuda paper pushes the envelope, but ''only'' comes up with trivial changes of variables. If you thought you found new ones which do not rely on implicitly ''defining'' new functions solving the Schroeder equation, you might well suggest them on this talk-page. [[User:Cuzkatzimhut|Cuzkatzimhut]] ([[User talk:Cuzkatzimhut|talk]]) 22:50, 4 October 2015 (UTC)

::ik this is very late but what does the Katsura and Fukuda say. [[Special:Contributions/100.2.153.196|100.2.153.196]] ([[User talk:100.2.153.196|talk]]) 02:00, 29 November 2023 (UTC)

:::also is there any way to access these papers without paying [[Special:Contributions/100.2.153.196|100.2.153.196]] ([[User talk:100.2.153.196|talk]]) 02:13, 29 November 2023 (UTC)

== Complex Iteration ==