Periodic Solutions of Some Problems of 3-Body Type

  • Abbas Bahri
  • Paul H. Rabinowitz
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 4)

Abstract

The study of time periodic solutions of the n-body problem is a classical one. See e.g 1 The purpose of this paper is to sketch some of our recent research on the existence of time periodic solutions of Hamiltonian systems of 3-body type [2] This work presents a new direct variational approach to the problem.

Keywords

Periodic Solution Hamiltonian System Unstable Manifold Homotopy Type Morse Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Poincaré, H., Les méthodes nouvelles de la mécanique céleste, Lib. Albert Blanchard, Paris, 1987.Google Scholar
  2. [2]
    Bahri, A. and P. H. Rabinowitz, Periodic solutions of Hamiltonian systems of 3-body type,to appear, Analyse Nonlinéaire.Google Scholar
  3. [3]
    Greco, C., Periodic solutions of a class of singular Hamiltonian systems, Nonlinear Analysis, T.M.A., 12, (1988), 259–270.MathSciNetMATHGoogle Scholar
  4. [4]
    Bahri, A. and P. H. Rabinowitz, A minimax method for a class of Hamiltonian systems with singular potentials, J. Functional Anal., 82, (1989), 412–428.MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    Bahri, A., work in preparation.Google Scholar
  6. [6]
    Hirsch, M. W., Differential Topology, Springer-Verlag 1975.Google Scholar
  7. [7]
    Bahri, A., Critical points at infinity in some variational problems,to appear, Pitman Research Notes in Mathematics.Google Scholar
  8. [8]
    Sullivan, D. and M. Vigué-Poirrier, The homology theory of the closed geodesic problem, J. Diff. Geom. 11, (1976), 633–644.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Abbas Bahri
    • 1
  • Paul H. Rabinowitz
    • 2
  1. 1.Mathematics DepartmentRutgers UniversityNew BrunswickUSA
  2. 2.Mathematics Department and Center for Mathematical SciencesUniversity of WisconsinMadisonUSA

Personalised recommendations