Modern Methods of Celestial Mechanics

Abstract

In connection with the 120th anniversary of the publication of the last volume of A. Poincare’s book “New Methods of Celestial Mechanics”, the following methods are considered that have arisen since then. 1. The normal form method, which allows one to study regular perturbations near a stationary solution, near a periodic solution, etc. 2. The method of truncated systems obtained with the help of Newton polyhedra, which allows the study of singular perturbations. 3. The method of generating families of periodic solutions (regular and singular). 4. Method of generalized problems admitting bodies with negative masses. 5. Calculation of the network of families of periodic solutions as a “skeleton” of a part of the phase space.