Global dynamics of planetary systems with the MEGNO criterion

In this paper we apply a new technique alternative to the numerically compu ted Lyapunov Characteristic Number (LCN) for studying the dynamical behavio ur of planetary systems in the framework of the gravitational N-body proble m. The method invented by P. Cincotta and C. Simo is called the Mean Expone ntial Growth of Nearby Orbits (MEGNO). It provides an efficient way for inv estigation of the fine structure of the phase space and its regular and cha otic components in any conservative Hamiltonian system. In this work we use it to study the dynamical behaviour of the multidimensional planetary syst ems. We investigate the recently discovered upsilon And planetary system, w hich consists of a star of 1.3 M. and three Jupiter-size planets. The two o utermost planets have eccentric orbits. This system appears to be one of th e best candidates for dynamical studies. The mutual gravitational interacti on between the two outermost planets is strong. Moreover the system can sur vive on a stellar evolutionary time scale as it is claimed by some authors (e.g., Rivera & Lissauer 2000b). As the main methodological result of this work, we confirm important properties of the MEGNO criterion such as its fa st convergence, and short motion times (of the order of 10(4) times the lon gest orbital period) required to distinguish between regular and chaotic be haviors. Using the MEGNO technique we found that the presence of the innerm ost planet may cause the whole system to become chaotic with the Lyapunov t ime scale of the order of 10(3)-10(4) yr only. Chaos does not induce in thi s case visible irregular changes of the orbital elements, and therefore its presence can be overlooked by studying variations of the elements. We conf irm explicitly the strong and sensitive dependence of the dynamical behavio ur on the companion masses.