The newest methods of celestial mechanics

The last volume of the book ‘‘Les méthods nouvelles de la mecanique céleste’’ by Poincaré was published 120 years ago. Since then, the following methods have arisen.

• Method of normal forms, allowing to study regular perturbations near a stationary solution, near a periodic solution and so on.
• Method of truncated systems, found with a help of the Newton polyhedrons, allowing to study singular perturbations.
• Method of generating families of periodic solutions (regular and singular).
• Method of generalized problems, allowing bodies with negative masses.
• Computation of a net of families of periodic solutions as a “skeleton” of a part of the phase space.