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Let ~ denote vector.

For a fixed point.

(~x0 is asymptotically stable if there exists

a neighbourhood U of ~x0 such that if ~x(t) obeys Hamilton's equations and ~x(0) in U, then lim

t->inf

~x(t) = ~x0.)

can you give me a precise definition for periodic solutions (limit cycles) in this context?

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# Limit Cycle

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