The Lyapunov stability in restricted problems of cosmic dynamics

Majority of cosmic dynamical problems are described by Hamiltonian systems. In this case the Lyapunov stability problem is the toughest problem of qualitative theory, but for two freedom degrees KAM–theory (Kolmogorov–Arnold–Moser methods) allows for the complete study [1–3]. For application of Arnold–Moser theorem [4] it is necessary to make finite sequence of Poincaré–Birkhoff canonical transformations [5] for Hamiltonian normalization. With the help of Symbolic System “Mathematica” [6] we determine the conditions of Lyapunov stability and instability of equilibrium points of restricted $n$–body problems [7].