Celestial Mechanics and Dynamical Astronomy

, Volume 113, Issue 4, pp 369–375 | Cite as

Some problems on the classical n-body problem

  • Alain Albouy
  • Hildeberto E. Cabral
  • Alan A. Santos
Special Report


Our idea is to imitate Smale’s list of problems, in a restricted domain of mathematical aspects of Celestial Mechanics. All the problems are on the n-body problem, some with different homogeneity of the potential, addressing many aspects such as central configurations, stability of relative equilibrium, singularities, integral manifolds, etc. Following Steve Smale in his list, the criteria for our selection are: (1) Simple statement. Also preferably mathematically precise, and best even with a yes or no answer. (2) Personal acquaintance with the problem, having found it not easy. (3) A belief that the question, its solution, partial results or even attempts at its solution are likely to have great importance for the development of the mathematical aspects of Celestial Mechanics.


n body problem Problems Central configurations Singularity 

Mathematics Subject Classification

70F10 70F15 


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Alain Albouy
    • 1
  • Hildeberto E. Cabral
    • 2
  • Alan A. Santos
    • 3
  1. 1.Astronomie et Systèmes Dynamiques, IMCCE, UMR 8028 du CNRSParisFrance
  2. 2.Departamento de MatemáticaUniversidade Federal de PernambucoRecifeBrazil
  3. 3.Departamento de MatemáticaUniversidade Federal de SergipeItabaianaBrazil

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