Wikipedia:Reference desk/Archives/Mathematics/2015 December 10
| Mathematics desk | ||
|---|---|---|
| < December 9 | << Nov | December | Jan >> | Current desk > |
| Welcome to the Wikipedia Mathematics Reference Desk Archives |
|---|
| The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
December 10
[edit]Chaotic systems with closed-form solutions
[edit]I know that in finite dimensions, a chaotic system has to be nonlinear, but are there any that have closed-form solutions? It seems like all the examples in the articles have to be solved numerically.--Jasper Deng (talk) 04:02, 10 December 2015 (UTC)
- Iterating f(x) = 4x(1−x) is chaotic and has the closed-form solution f n(x) = sin2(2n arcsin(√x)), as stated in Iterated_function#Examples and Schröder's_equation#Applications. Egnau (talk) 15:27, 10 December 2015 (UTC)
- I was more looking for one defined in 3 dimensions by a differential equation (i.e. not a discrete case), but this provides enough intuition, thanks.--Jasper Deng (talk) 22:45, 11 December 2015 (UTC)