# To see if a system behaves chaotically does one have to vary (in a tiny way) the initial momenta of ALL constituents of the system?

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).

• Atoms aren't part of the usual model for the double pendulum, but yes, nearby trajectories diverge exponentially fast, so no matter how tiny the initial separation - including one of, say, $10^{-22}$ - one will observe them diverge eventually. I don't know any specific model for a waterfall off the top of my head, but what you describe should admit some chaotic models, perhaps even some displaying spatial-temporal chaos, pattern formation, etc. – stafusa Jun 18 '19 at 14:52