4 Recherche d'orbites périodiques d'un champ hamiltonien associé à une structure symplectique non standard

Gérard Grangier

Publications du Département de mathématiques (Lyon) (1984)

  • Volume: 3/B, Issue: 3B, page 65-78
  • ISSN: 0076-1656

How to cite

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Grangier, Gérard. "4 Recherche d'orbites périodiques d'un champ hamiltonien associé à une structure symplectique non standard." Publications du Département de mathématiques (Lyon) 3/B.3B (1984): 65-78. <http://eudml.org/doc/274229>.

@article{Grangier1984,
author = {Grangier, Gérard},
journal = {Publications du Département de mathématiques (Lyon)},
keywords = {cotangent bundle; Hamiltonian system; Legendre transformation; periodic orbits of a Hamiltonian vector field; magnetic symplectic form; variational principles},
language = {fre},
number = {3B},
pages = {65-78},
publisher = {Université Claude Bernard - Lyon 1},
title = {4 Recherche d'orbites périodiques d'un champ hamiltonien associé à une structure symplectique non standard},
url = {http://eudml.org/doc/274229},
volume = {3/B},
year = {1984},
}

TY - JOUR
AU - Grangier, Gérard
TI - 4 Recherche d'orbites périodiques d'un champ hamiltonien associé à une structure symplectique non standard
JO - Publications du Département de mathématiques (Lyon)
PY - 1984
PB - Université Claude Bernard - Lyon 1
VL - 3/B
IS - 3B
SP - 65
EP - 78
LA - fre
KW - cotangent bundle; Hamiltonian system; Legendre transformation; periodic orbits of a Hamiltonian vector field; magnetic symplectic form; variational principles
UR - http://eudml.org/doc/274229
ER -

References

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  1. [1] R. Abraham and J.E. Marsden, Foundations of Mechanics (2ème édition) Benjamin (1978) p. 218-251. Zbl0393.70001MR515141
  2. [2] C. Grenberg, Lectures on algebraic topology, Benjamin (1967). Zbl0169.54403MR215295
  3. [3] W. Klingenberg, Lectures on closed geodesics, Springer (1978). Zbl0397.58018MR478069
  4. [4] J.P. Mesirov, Perturbation theory for condition (C) in the calculus of variation, J. differential geometry12 (1977), p. 523-533. Zbl0388.58007MR512923
  5. [5] S.P. Novikov and I. Shmel'ster, Periodic solution of Kirchoff equations for the free motion of rigid body in a fluid and the extended theory of Lyusternik-Schnirel'mann Morse (I). Funct. Anal. Priloztien15 n°3, traduction américaine (1982), p. 197-207. Zbl0571.58009
  6. [6] R. Palais, Lusternick-Schnirel'mann theory on Banach manifold, Topology5 (1966), p. 115-132. Zbl0143.35203MR259955
  7. [7] R. Palais and S. Smale, A generalised Morse theory : Bull. Amer. Math. Soc.70 (1964), p. 165-171. Zbl0119.09201MR158411
  8. [8] P.H. Rabinowitz, Periodic solutions of Hamilton systems, Comm. on Pure and Applied Maths., vol. XXXI (1978), p. 157-184. Zbl0358.70014MR467823
  9. [9] J.T. Schwartz, Non linear functional analysis, Gordon and Breach (1969). Zbl0203.14501
  10. [10] S. Smale, Morse theory and a non linear generalisation of the dirichlet problem, Ann. Math.80 (1964), p. 382-396. Zbl0131.32305MR165539
  11. [11] J.M. Souriau, Structures des systèmes dynamiques, Dunod (1975). Zbl0186.58001
  12. [12] A. Weinstein, Symplectic manifold and their lagrangien submanifold, Advances in maths (1971), p. 329-345. Zbl0213.48203MR286137

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