PERIODIC ORBITS IN GRAVITATIONAL SYSTEMS

摘要

The periodic orbits play an important role in the study of the stability of a dynamical system. The methods of study of the stability of a periodic orbit are presented both in the general case and for Hamil-tonian systems. The Poincare map on a surface of section is presented as a powerful tool in the study of a dynamical system, especially for two or three degrees of freedom. Special attention is given to nearly integrable dynamical systems, because our solar system and the extra solar planetary systems are considered as perturbed Keplerian systems. The continuation of the families of periodic orbits from the unperturbed, integrable, system to the perturbed, nearly integrable system, is studied.