The three- and the N-body problem
type: Dataset
contact point: Organization
  fn: CCSD
keyword: instability
keyword: lagrangian-action
keyword: reduction
keyword: integrability
keyword: differential-galois-theory
keyword: newtons-equation
keyword: chazys-classification
keyword: first-integral
keyword: small-denominators
keyword: lagrange-and-laplace-stability-theorems
keyword: lindstedt-series
keyword: homographic-motions
keyword: marchal-chenciners-theorem
keyword: poincares-classification
keyword: sundmans-inequality
keyword: choreography
keyword: book-sections
keyword: monodromy-group
keyword: transverse-heteroclinic-intersection
keyword: periodic-orbit
keyword: birkhoff-series
keyword: collision
keyword: non-collision-singularity
keyword: figure-eight-solution
keyword: planetary-problem
keyword: lagrange-jacobi-identity
keyword: regularization
keyword: arnolds-theorem
keyword: quasi-periodic-orbit
keyword: infoeu-reposemanticsbookpart
keyword: final-motions
keyword: hills-problem
keyword: mathmath-dsmathematics-mathdynamical-systems-mathds
keyword: kam-theory
keyword: von-zeipel-series
keyword: nekhoroshev-theorem
keyword: stability
keyword: relative-equilibria
keyword: symmetry
keyword: central-configuration
keyword: symbolic-dynamics
keyword: homothetic-motion
keyword: conley-wintner-endomorphism
landing page: Celestial Mechanics
description: We introduce the $N$-body problem of mathematical celestial mechanics, and discuss its astronomical relevance, its simplest solutions inherited from the two-body problem (called homographic motions and, among them, homothetic motions and relative equilibria), Poincaré's classification of periodic solutions, symmetric solutions and in particular choreographies such as the figure-eight solution, some properties of the global evolution and final motions, Chazy's classification in the three-body problem, some non-integrability results, perturbations series of the planetary problem and a short account on the question of its stability.
issued: 2026-05-07T22:08:27.936882
language: en
modified: 2026-05-07T22:08:27.936887

The three- and the N-body problem
type: Distribution
access URL: https://hal.science/hal-00915271
format: HTML
issued: 2026-05-07T22:08:27.957125
modified: 2026-05-07T22:08:27.898324

test_moissonnage_selune
type: Agent