Comment on [deleted]
vrighter@discuss.tchncs.de 3 weeks agoI completely agree with what this comment says. It’s still irrelevant though. Where did I say it has to be unbounded? You are countering an argument I did not make. Whether the result is divergent or not is irrelevant. The point is that “not having a closed form solution” is not the meaning of chaos, which was your original wrong statement.
Blue_Morpho@lemmy.world 3 weeks ago
No closed form solution is one property. It’s not wrong, only incomplete. But if a system of equations had a closed form solution, it wouldn’t be called chaotic. For example any exponential equation like x^y is extremely sensitive to initial conditions yet it isn’t chaotic.
vrighter@discuss.tchncs.de 3 weeks ago
oh really?
Blue_Morpho@lemmy.world 3 weeks ago
'Robert L. Devaney, says that to classify a dynamical system as chaotic, it must have these properties:[22]
it must be sensitive to initial conditions, it must be topologically transitive, it must have dense periodic orbits. " en.m.wikipedia.org/wiki/Chaos_theory
f(x)=x^y doesn’t satisfy those 3 conditions. Nor does the paper you link say that either.
vrighter@discuss.tchncs.de 3 weeks ago
and again, in the definition you just pasted in there does not say anything about closed form solutions. You keep contradicting yourself in trying to die on that hill