Periodic solutions for the N-body problem: a variational approach
Abstract:
The purpose of the lectures is to introduce to
the variational approach to the search of periodic solutions for the N-body
problems. Such an approach has recently lead to the discovery of
some new periodic solutions (see, for example, the paper A. Chenciner
and
R. Montgomery, A remarkable periodic solution of the three-body problem in the case of equal masses, Ann. of Math. (2), 152 (2000), 881--901). |
1. Introduction, central configurations. |
2. The variational approach and the minimizing properties of the solutions of the 2-body problem and of the central configurations. |
3. The lack of compactness of the variational formulation for the 2 and the N-body problem. Symmetry and topological constrains. |
4. Collisions, strong and weak forces. |
5. Existence of periodic non-collision solutions via
variational methods for perturbed N-body problems. |
6. Existence of periodic solutions for the N-body problem: symmetry and variational constrains. |