A very tiny change in the initial data may rapidly give rise to an absolutely enormous change in the resulting behaviour. (Anyone who has tried to pocket a billiard ball, by hitting it with an intermediate ball that has to be hit first, will know what I mean!) This is particularly apparent when (successive) collisions are involved, but such instabilities in behaviour can also occur with Newtonian gravitational action at a distance (with more than two bodies). The term ‘chaos’, or ‘chaotic behaviour’ is often used for this type of instability. Chaotic behaviour is important, for example, with
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