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What does it mean for a phase space trajectory to be "long" and "stable"?

I understand the concept of a trajectory in phase space but not how these adjectives can be applied to one.

Thanks.

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In most contexts "stable" means that small perturbations of the initial conditions result in bounded changes to the final state. Contrast this to "sensitive dependence on initial conditions". –  dmckee Sep 30 '11 at 1:24
    
Can you please provide context? –  Ron Maimon Oct 10 '11 at 5:33
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