>As a thought experiment, stand up two instances: one is our current situation ..., the other where we have (somehow) proven out ... that a closed form solution is not possible
As far as I understand, this has in fact been proved. Quite a long time ago, too, by Poincare I believe.
GP has edited his comment to reflect my feedback, but originally said that his experiment "demonstrates that there is no solution." All I was trying to point out is that the two concepts are not necessarily related.
You could imagine some system x' = f(x), where f(x) is some transcendental function. There is no analytic solution to this system, but it's obviously not chaotic.
>As a thought experiment, stand up two instances: one is our current situation ..., the other where we have (somehow) proven out ... that a closed form solution is not possible
As far as I understand, this has in fact been proved. Quite a long time ago, too, by Poincare I believe.
GP has edited his comment to reflect my feedback, but originally said that his experiment "demonstrates that there is no solution." All I was trying to point out is that the two concepts are not necessarily related.
You could imagine some system x' = f(x), where f(x) is some transcendental function. There is no analytic solution to this system, but it's obviously not chaotic.
Could you imagine a system that is chaotic but does have an analytical solution? I'm not sure. Closest I could find to answering this was: https://sprott.physics.wisc.edu/pubs/paper496.pdf
I'm sure he understood this. I only commented to try and minimize the confusion of others.
edit - This article suggests that the logistic map (a system famously used to introduce the concept of chaos) has an analytical solution: https://www.sciencedirect.com/science/article/pii/0378437195...