Inventiones mathematicae

, Volume 20, Issue 1, pp 59–72

On the integral manifolds of theN-body problem

  • H. E. Cabral


Here we make a topological study of the mapI=(E, J), whereE is the energy andJ is the angular momentum of then-body problem in 3-space. Part of the bifurcation set ofI is characterized and some topological information is given on the integral manifolds of negative energy and zero angular momentum.


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  1. 1.
    Birkhoff, G. D.: Dynamical Systems. Rev. Ed. Colloq. Publ.9, Amer. Math. Soc., Providence, R. I., 1966.Google Scholar
  2. 2.
    Easton, R.: Some Topology of the 3-Body Problem. Journal of Differential Equations10, 371–377 (1971).Google Scholar
  3. 3.
    Lang, S.: Introduction to Differentiable Manifolds. New York: Wiley (Interscience) 1962.Google Scholar
  4. 4.
    Robbin, J. W.: Relative Equilibria in Mechanical Systems. Preprint. Univ. of Wisconsin, Madison, Wis.Google Scholar
  5. 5.
    Smale, S.: Topology and Mechanics. I. Inventiones math.10, 305–331 (1970).Google Scholar
  6. 6.
    Smale, S.: Topology and Mechanics, II. Inventiones math.11, 45–64 (1970).Google Scholar
  7. 7.
    Spanier, E. H.: Algebraic Topology. New York: McGraw-Hill 1966.Google Scholar
  8. 8.
    Wintner, A.: The Analytical Foundations of Celestial Mechanics. Princeton, N. J.: Princeton Univ. Press 1941.Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • H. E. Cabral
    • 1
  1. 1.Instituto de Matematica Pura e AplicadaRio de JaneiroBrasil

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