Limit Cycle


    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
    ~x(t) = ~x0.)

    can you give me a precise definition for periodic solutions (limit cycles) in this context?
  2. jcsd
  3. A solution x is periodic iff there exists T >0 with x(t+T) = x(t) for all t.
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