Talk:Chaos theory/Archive 5
I don't know if the butterfly should really have its own page as it is only an example of chaos theory
Does anyone here besides me think that fractals deserve some mention in the article?
Fractals could indeed be mentioned if strange attractors where also mentioned. I'd do it myself if it weren't because someone else seems to be editing the page right now (concurrent editing is a pain, even under WikiWiki :).
Regarding the Lorenz attractor, take a pick on http://www.google.com/search?q=Lorenz+attractor.
--Filip Larsen
- I think the statement "Strange attractors have a fractal-like structure." might be too strong. I don't think that is proven. --jkominek
Please tell me that real academics don't use the word "dynamical". The "ic" and "al" suffixes mean the same thing (they both mean "pertaining to"). It's just like nails on a chalkboard to me, especially considering that looking the word up in a dictinoary yields the definition "see dynamic".
- Real academics might not use the word, but mathematicians certainly do. "Dynamical systems" is what it's called everywhere. --Axelboldt
- Just looked it up in the OED. ::sigh:: stinking Greek word not adhering to the system of short roots everywhere else in english...
This Artical does also not mention using the logistic equation to generate (pseudo)random numbers, nor does the artical on pseudorandom numbers mentions chaos theory. Both of which are interesting, as numbers generated in such a manor would theoretically have no period.
I'm new, so I still don't know how does it work. Senzitivity on initial conditions and boundedness are not enough to get chaotic motion. They can imply for instance Quasi-periodicity. In 2D continuous dynamical systems you can have both conditions fullfiled and you"ll stil wont get a chaos. I also think that Entropy should necessary be mentioned on this page.
mention of knot theory as well?
- Knot theory is more a branch of topology, not of chaos theory. AxelBoldt 22:13 Sep 26, 2002 (UTC)
This article seems to address the general issue of nonlinear dynamical systems, of which chaos theory forms a subset. I think it should be made VERY clear that the fields of nonlinear dynamics and chaos theory are NOT the same -- nonlinear dynamics deals with any dynamical system that displays nonlinear behavior. ONE of these types of systems is a chaotic system. However, a choatic system is a VERY SPECIFIC type of nonlinear system, it is a system that must satisfy a very specific set of properties, e.g. as set out in the original paper with that title something like "period 3 implies chaos" that started the whole thing. However, NOT every nonlinear system is chaotic, and confusing the two, implying that "chaos theory" and "nonlinear dynamics" are equivalent (which is a very common thing that people do) is not correct and gives a very misleading impression.
The origins of chaos theory go much farther back than the 1950s. Similar problems were studied by Poincare, Kolmogorov, and others. Mathematicians were thinking about this long before experimentalists "discovered" it. The math was just very difficult to read and lacked intuition because the physics hadn't caught up.