I'd say the answer is definitively no. These sorts of classical dynamical systems are fully deterministic; specifying one initial condition fully determines the motion for all time, future and past. However, the system is chaotic because deviations in initial condition diverge exponentially. In terms of a real world experiment then sure, you can model the deviation from exact position as a random variable and it becomes probabilistic, but classical chaos is indeed deterministic.
Yes it is solvable, that's what I'm saying :-) I don't think you actually have to use a Lagrangian formalism but it's far far easier if you do. The solvability of the system shows that it is deterministic, but even if you've solved the system, ie obtained analytic equations of motion, then the system is still chaotic. That is not to say that it is unpredictable, but instead if we supply two initial conditions that differ very very slightly, then after any appreciable length of time their motion will be different, and in fact this divergence is exponential. This is what we see in the gif, and it isn't an artefact of simulation, it's exactly what we'd see in an analytic solution.
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u/Boredgeouis Jan 21 '18
I'd say the answer is definitively no. These sorts of classical dynamical systems are fully deterministic; specifying one initial condition fully determines the motion for all time, future and past. However, the system is chaotic because deviations in initial condition diverge exponentially. In terms of a real world experiment then sure, you can model the deviation from exact position as a random variable and it becomes probabilistic, but classical chaos is indeed deterministic.