That’s a really cool proof, but phase space can be exponentially large, especially for an “extremely complicated” system. It also requires finite bounds on system parameters.
For that to break my “extremely high probability”, there would have to be relatively few orbits in the phase space approaching a space-filling set of curves, which is itself extremely unlikely, unless you can think up some pathological example.
That’s a really cool proof, but phase space can be exponentially large, especially for an “extremely complicated” system. It also requires finite bounds on system parameters.
For that to break my “extremely high probability”, there would have to be relatively few orbits in the phase space approaching a space-filling set of curves, which is itself extremely unlikely, unless you can think up some pathological example.
It does weaken my statement, though.