ABSTRACT
Therefore there is a simple criterion to prove the possible existence of a third integral ¢ , namely: If the successive points of intersection P, of the phase trajectory with the plane of section (z = 0 ) lie on an invariant curve, then there exists a third isolating integral. In the opposite case, by following the phase trajectory with a known energy E during a longer and longer time these points P, will fill an area detennined by the condition:
t;e+U(x,o)~E which represents the intersection ofdomain n by the plane of section.
