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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Albouy, Alain and Kaloshin, Vadim 2012. Finiteness of central configurations of five bodies in the plane. Annals of Mathematics, Vol. 176, Issue. 1, p. 535.

    Alfaro, Felipe and Perez-Chavela, Ernesto 2008. Linear stability of relative equilibria in the charged three-body problem. Journal of Differential Equations, Vol. 245, Issue. 7, p. 1923.

    Roberts, Gareth E. 1999. A continuum of relative equilibria in the five-body problem. Physica D: Nonlinear Phenomena, Vol. 127, Issue. 3-4, p. 141.

    McCord, Christopher K. 1996. Planar central configuration estimates in the n-body problem. Ergodic Theory and Dynamical Systems, Vol. 16, Issue. 05, p. 1059.

    Smale, Steve 1991. Dynamics retrospective: great problems, attempts that failed. Physica D: Nonlinear Phenomena, Vol. 51, Issue. 1-3, p. 267.

    Moeckel, Richard 1990. On central configurations. Mathematische Zeitschrift, Vol. 205, Issue. 1, p. 499.

    Meyer, Kenneth R. and Schmidt, Dieter S. 1988. Bifurcations of Relative Equilibria in theN-Body and Kirchhoff Problems. SIAM Journal on Mathematical Analysis, Vol. 19, Issue. 6, p. 1295.

  • Ergodic Theory and Dynamical Systems, Volume 5, Issue 3
  • September 1985, pp. 417-435

Relative equilibria of the four-body problem

  • Richard Moeckel (a1)
  • DOI:
  • Published online: 01 September 2008

By employing a regularizing transformation, the problem of bifurcation of relative equilibria in the Newtonian 4-body problem is reduced to a study of an algebraic correspondence between real algebraic varieties. The finiteness theorems of algebraic geometry are used to find an upper bound for the number of affine equivalence classes of relative equilibria which holds for all masses in the complement of a proper, algebraic subset of the space of all masses.

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Ergodic Theory and Dynamical Systems
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