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Great article; I learnt that Arnol'd tongues can in fact be described in very simple language. However, I have the distinct impression that "circle map" refers to any map from the circle to itself. I think the map described here is usually called the "sine circle map" (though I've also seen "sine map"). -- Jitse Niesen (talk) 11:52, 19 January 2006 (UTC)
- I think the chaos literature is pretty consisent in using "circle map" to refer to only this map, although I've seen the more general definition on occasion. The only support I have for this at the moment is the MathWorld article, and the refs that it cites. linas 23:36, 19 January 2006 (UTC)
- I agree with Nitse. A "circle map" can be any map of the circle. The confusion might come from the fact that the standard maps described by Arnol'd essentially model the behavior of many circle maps, up to topological conjugacy.
I renamed article to Arnold tongues per the discussion above. The term circle map can certainly refer to any map of a circle, and there are various researches devoted to study of circle maps, see e.g. Katok-Hasselblat. The family exposed can be named standard circle maps family or something like this, but I believe Arnold tongues is the main subject of the paper. Ilya Voyager (talk) 15:52, 5 September 2012 (UTC)
- ....and I changed it to Arnold tongue since WP:MOS clearly says the singular should be used except when there's a reason to use the plural. Michael Hardy (talk) 03:56, 6 September 2012 (UTC)
Beating heart model
How does the circle map correspond to a model of the beating heart? If this could be explained briefly and in language suitable for a layman, possibly in a section of its own (near the end of the article?), that would be excellent. --Quuxplusone 17:14, 16 April 2006 (UTC)
Who is the eponym??
Is this named after Vladimir Arnold? If not, who's it named after? It is unconscionable that that question is not answered. It should be in the first line. Michael Hardy (talk) 04:11, 6 September 2012 (UTC)
- For those who haven’t seen - see WP Maths. Maschen (talk) 16:39, 6 September 2012 (UTC)
Can't understand the article... where to go to get the basics first... can't Wikipedia have this section "textbook / prerequisites" for all mathematical/technical articles. 184.108.40.206 (talk) 08:42, 27 October 2012 (UTC)
In the second image, with the subtitle "Some of the Arnold tongues for the standard circle map, ", shouldn't alpha by Omega on the horizontal axis? And the comma a period in the subtitle? — Preceding unsigned comment added by Mmbosschaert (talk • contribs) 16:33, 20 January 2013 (UTC)