Talk:Sarkovskii's theorem

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Can someone point me to an accessible version of the proof of this theorem ? I have tried looking on arxiv etc. to add it to the page, but have been unlucky so far. AmarChandra 17:00 May 23, 2004 (UTC)

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stable cycles appear in Sarkovskii order in the bifurcation diagram, starting with 1 and ending with 3, as the parameter is varied. - I doubt that this is true. Isn't there bifurcation after 3, leading to stable cycles of period 6 for slightly larger parameters?

Also, Sarkovskii's theorem doesn't say anything about the way the period of stable cycles change as the parameter changes, so I think this statement, even if true, confuses the matter. AxelBoldt 01:46 Sep 30, 2002 (UTC)

There are stable cycles of various orders, including 5 as well as 6, 12, ..., after the 3-cycle. What counts is the first time the cycle appears. -phma

Oh, ok, I'll put the statement back then. AxelBoldt 21:26 Dec 22, 2002 (UTC)

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We should move this term Sarkovskii's theorem to proper term Sharkovsky's theorem, since it is named after Ukrainian mathematician Oleksandr Mikolaiovich Sharkovsky and hence goes the English spelling. Best regards. --XJam 12:27 Dec 17, 2002 (UTC)

Google gives about three times as many hits for Sarkovskii's theorem than for Sharkovsky's theorem, so I suggest we leave the article at the more common spelling. AxelBoldt 21:26 Dec 22, 2002 (UTC)

I disagree in full. Bad habit. Don't mind the Google. Thousand times spoken lie becomes a truth. If Google is wrong, why should be Wikipedia then too. And still, if we translate his first name in English, we should write Olexandr and, I guess, not Oleksandr. But as it seems, nobody cares that. Nevertheless we should be even more precise here. That is my strong opinion. --XJam 23:32 Dec 23, 2002 (UTC)

Why do you think that Sarkovskii is wrong and Sharkovsky is right? AxelBoldt 02:49 Dec 24, 2002 (UTC)

I believe the spelling Sarkovskii comes from other languages than English, probably mostly from French and German language. Have you checked searching Sharkovsky just in Google's English pages? I haven't. But I guess it would give more terms than Sarkovskii. In Slavic languages a letter "s" is completely different from a letter "sh". I tried to find a person, who is responsible for this theorem under Sarkovskii, but I failed. It was just my lucky guess that I really found him. But I might be wrong after all too. I am just trying to be accurate as posible as I can. Someone is more careful regarding strictly math terms and someone regarding related math terms as names, surnames, birthplaces and such are. --XJamRastafire 10:36 Dec 24, 2002 (UTC)

Actually, I've seen Šharkovksii for the Ukrainian spelling. I agree that the best English spelling is probably Sharkovsky. Also, I have seen some experienced Wikipedians argue that articles about theorems should be named X theorem rather than X's theorem, although I am not sure I agree. One thing seems clear: whatever the name of the article, someone should ensure that there are suitable redirects from the other candidates. ---CH 21:02, 13 May 2006 (UTC)