A. Celletti et P. Negrini, NONINTEGRABILITY OF THE PROBLEM OF MOTION AROUND AN OBLATE PLANET, Celestial mechanics & dynamical astronomy, 61(3), 1995, pp. 253-260
We provide a result of non-analytic integrability of the so-called J(2
)-problem. Precisely by using the Lerman theorem we are able to prove
the existence of a region of the phase space, where the dynamical syst
em exhibits chaotic motions.