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Periodic solutions of prescribed energy of hamiltonian systems

  • Paul H. Rabinowitz
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1324)

Keywords

Periodic Solution Hamiltonian System Ordinary Differential Equation Model Interesting Open Question Prescribe Energy 
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.

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References

  1. [1]
    Seifert, H., Periodische Bewegungen mechanischen Systeme, Math. Z., 51, (1948), 197–216.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Weinstein, A., Periodic orbits for convex Hamiltonian systems, Ann. Math. 108, (1978), 507–518.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Clarke, F., A classical variational principle for periodic Hamiltonian trajectories, Proc. Amer. Math. Soc. 76, (1979), 186–188.MathSciNetzbMATHGoogle Scholar
  4. [4]
    Rabinowitz, P. H., Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math., 31, (1978), 157–184.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Rabinowitz, P.H., Periodic solutions of a Hamiltonian system on a prescribed energy surface, J. Diff. Eq., 33, (1979), 336–352.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Gluck, H. and W. Ziller, Existence of periodic solutions of conservative systems, Seminar on Minimal Submanifolds, Princeton Univ. Press, (1983), 65–98.Google Scholar
  7. [7]
    Hayashi, K., Periodic solution of classical Hamiltonian systems, Tokyo J. Math., 6, (1983), 473–486.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Benci, V., Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural Hamiltonian systems, Ann. Inst. H. Poincare. Analy. Nonlineaire.Google Scholar
  9. [9]
    Rabinowitz, P. H., On the existence of periodic solutions for a class of symmetric Hamiltonian systems, to appear: Nonlinear Analysis, T.M.A.Google Scholar
  10. [10]
    Ekeland, I. and J. M. Lasry, On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface, Ann. Math., 112, (1980), 283–319.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    van Groesen, E. W. C., Existence of multiple normal mode trajectories on convex energy surfaces of even classical Hamiltonian systems, to appear, J. Diff. Eq.Google Scholar
  12. [12]
    Girardi, M., Multiple orbits for Hamiltonian systems on starshaped surfaces with symmetries, Ann. Inst. H. Poincare, Analy. Nonlineaire, 1 (1984), 285–294.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Paul H. Rabinowitz
    • 1
  1. 1.Mathematics Department and Mathematics Research CenterUniversity of WisconsinMadisonUSA

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