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