Talk:Dynamical system

The term discrete dynamical system redirects here, but there is (almost) no discussion of the topic here. Would be nice for somebody to write it. Dmharvey Talk 19:43, 5 July 2005 (UTC) [reply ]

I changed the definition back. A dynamical system is a smooth function from a manifold to itself dependent on one parameter, time. While the manifold could be replaced by a more general set, loosing smoothness takes one to ergodic theory or symbolic dynamics. The parameter needs to be a monoid traditionally written in additive form. One could just formalize that definition, but the challenge is to re-write it so that someone with high school mathematics can follow the definition.

From what I replaced, I liked the use of relationship instead of function and responding to their own values, which emphasizes the mapping a point of the manifold back onto itself. But I could not get it to work. Maybe someone else could try. XaosBits (talk) 05:53, 29 December 2015 (UTC) [reply ]

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Finite time solutions are an extreme opposite of ergodic behavior. Nonlinear and chaotic systems are not a subclass of ergodic systems. Finite time solutions do require nonlinearity. The organization here therefore makes very little sense. RowanElder (talk) 13:47, 29 September 2024 (UTC) [reply ]