Round-off sensitivity in the N-body problem

  • Herwig Dejonghe
  • Piet Hut
Poster Session
Part of the Lecture Notes in Physics book series (LNP, volume 267)


The solutions to the equations of motion of the gravitational N-body problem are extremely sensitive to very small changes in initial conditions, resulting in a near-exponential growth of deviations between neighboring trajectories in the system’s 6N-dimensional global phase space. We have started to investigate the character of this instability, and the relative contributions to the exponential growth given by two-body, three-body, and higher-order encounters. Here we present our first results on 3-body scattering, where we measured the total amplification factor of small perturbations in the initial conditions.


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  1. Alexander, M.E., 1986. Journal Comp. Phys., 64, p 195.MATHCrossRefADSGoogle Scholar
  2. Birkhoff, G.D., 1927. Dynamical Systems, Am. Math. Soc. Publ., Providence, R.I.Google Scholar
  3. Heggie, D.C., 1973. Celestial Mech., 10, p 217.CrossRefADSGoogle Scholar
  4. Hut, P. and Bahcall, J.N., 1983, Astrophys. J. 268, p 319.CrossRefADSGoogle Scholar
  5. Mikkola, S., 1985. Mon. Not. R. Astr. Soc., 215, p 271.ADSMathSciNetGoogle Scholar
  6. Miller, R.H., 1964. Ap. J., 140, p 250.CrossRefADSGoogle Scholar
  7. Stiefel, E.L. and Scheifele, G., 1971. Linear and Regular Celestial Mechanics, Springer Verlag, Berlin.MATHGoogle Scholar
  8. Szebehely, V., 1973. Recent Advances in Dynamical Astronomy, Tapley B.D. and Szebehely, V. eds, p 75.Google Scholar
  9. Szebehely, V. and Peters F., 1976. Astron. J., 72, p 876.CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Herwig Dejonghe
    • 1
  • Piet Hut
    • 1
  1. 1.The Institute for Advanced StudyPrinceton

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