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Consider a deterministic system (a gas, a liquid, or a solid, each of which can have an arbitrary form; for example, the atmosphere, a waterfall, or a double pendulum) which consists of a huge number of constituents like atoms or molecules, which have a certain distribution of their momenta.

To see if the system behaves chaotically do we have to vary the momenta of all its constituents in a tiny (and in the same) way to see if the system behavior is chaotic, or can we just vary the momenta of a tiny portion of the system?

I ask this because in an answer to a question I read that varying a little piece of the weather system would imply that the weather system is a chaotic phenomenon (which it obviously is).

stafusa
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Nope. One certainly doesn't have to vary a huge number of system variables to test for divergence of trajectories (i.e., the sensitivity to initial conditions characteristic of chaos) - changing a single one is sufficient.

That's what justifies the famous hyperbole "Does the flap of a butterfly's wing in Brazil set off a tornado in Texas?", already covered in Physics SE here - whose answer, by the way, is "Well, yes, but it can also prevent the tornado or have a completely different effect (including nothing remarkable), just like every one of the innumerable arbitrarily small perturbations the system is constantly subjected to.".

stafusa
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