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?