Sujet

Newton's equation; symmetry; reduction; Conley-Wintner endomorphism; stability; planetary problem; Hill's problem; central configuration; homographic motions; relative equilibria; homothetic motion; periodic orbit; Poincaré's classification; choreography; figure-eight solution; Lagrangian action; Lagrange-Jacobi identity; Sundman's inequality; collision; regularization; Marchal-Chenciner's theorem; non-collision singularity; final motions; Chazy's classification; integrability; first integral; transverse heteroclinic intersection; monodromy group; differential Galois theory; Lindstedt series; von Zeipel series; small denominators; Birkhoff series; Lagrange and Laplace stability theorems; Arnold's theorem; quasi-periodic orbit; Nekhoroshev theorem; KAM theory; instability; symbolic dynamics