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## Main Question or Discussion Point

http://books.google.ca/books?id=Pd8...ook_result&ct=result&resnum=1&ved=0CAkQ6AEwAA

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?

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?