Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural hamiltonian systems

V. Benci

Annales de l'I.H.P. Analyse non linéaire (1984)

  • Volume: 1, Issue: 5, page 401-412
  • ISSN: 0294-1449

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Benci, V.. "Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural hamiltonian systems." Annales de l'I.H.P. Analyse non linéaire 1.5 (1984): 401-412. <http://eudml.org/doc/78083>.

@article{Benci1984,
author = {Benci, V.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {mechanical system; Hamiltonian system; periodic solution},
language = {eng},
number = {5},
pages = {401-412},
publisher = {Gauthier-Villars},
title = {Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural hamiltonian systems},
url = {http://eudml.org/doc/78083},
volume = {1},
year = {1984},
}

TY - JOUR
AU - Benci, V.
TI - Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural hamiltonian systems
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1984
PB - Gauthier-Villars
VL - 1
IS - 5
SP - 401
EP - 412
LA - eng
KW - mechanical system; Hamiltonian system; periodic solution
UR - http://eudml.org/doc/78083
ER -

References

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  1. [AM] A. Ambrosetti, G. Mancini, On a theorem by Ekeland and Lasry concerning the number of periodic Hamiltonian trajectories. J. Diff. Equ., t. 43, 1981, p. 1-6. Zbl0492.70018
  2. [A] V.I. Arnold, Méthodes mathématiques de la mécanique classique, Éditions Mir, Moscou, 1976. Zbl0385.70001MR474391
  3. [B] V. Benci, Normal modes of a Lagrangian system constrained in a potential well, Ann. Inst. H. Poincaré, t. 1, 1984, p. 379-400. Zbl0561.58006MR779875
  4. [Br] H. Berestycki, Solutions périodiques des systèmes Hamiltoniens. Séminaire N. Bourbaki, Volume 1982-1983. [BLMR] H. Berestycki, J.M. Lasry, G. Mancini, R. Ruf, Existence of multiple periodic orbits on star-shaped hamiltonian surfaces. Preprint. 
  5. [EL] I. Ekeland, J.M. Lasry, On the number of periodic trajectories for a hamiltonian flow on a convex energy surface, Ann. Math., t. 112, 1980, p. 283-319. Zbl0449.70014MR592293
  6. [GZ] H. Gluck, W. Ziller, Existence of periodic motions of conservative systems, in Seminar on Minimal Submanifold, E. Bombieri Ed., Princeton University Press, 1983. Zbl0546.58040MR795229
  7. [G] H. Goldstain, Classical Mechanics, Addison-Wesley, 1981. 
  8. [H] K. Hayashi, Periodic solutions of classical Hamiltonian systems, Tokyo J. Math., t. 6, 1983. Zbl0498.58010MR732099
  9. [M] J. Moser, Periodic orbits near an equilibrium and a theorem by A. Weinstein, Comm. Pure Appl. Math., t. 29, 1976, p. 727-747. Zbl0346.34024
  10. [R1] P.H. Rabinowitz, Periodontic solutions of Hamiltonian systems' a survey, SIAM J. Math. Anal., t. 13, 1982. Zbl0521.58028MR653462
  11. [R2] P.H. Rabinowitz, Periodic solutions of a Hamiltonian system on a prescribed energy surface, J. Differential Equations, t. 33, 1979, p. 336-352. Zbl0424.34043MR543703
  12. [S] H. Seifert, Periodischer bewegungen mechanischer Systeme, Math. Zeit., t. 51, 1948, p. 197-216. Zbl0030.22103MR25693
  13. [W] A. Weinstein, Normal modes for nonlinear Hamiltonian systems, Invent. Math., t. 20, 1973, p. 47-57. Zbl0264.70020MR328222

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