Transition le long des chaînes de tores invariants pour les systèmes hamiltoniens analytiques

Jean-Pierre Marco

Annales de l'I.H.P. Physique théorique (1996)

  • Volume: 64, Issue: 2, page 205-252
  • ISSN: 0246-0211

How to cite

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Marco, Jean-Pierre. "Transition le long des chaînes de tores invariants pour les systèmes hamiltoniens analytiques." Annales de l'I.H.P. Physique théorique 64.2 (1996): 205-252. <http://eudml.org/doc/76713>.

@article{Marco1996,
author = {Marco, Jean-Pierre},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {lambda-lemma; existence of orbits; extremal tori; normal form; transition time; Easton's windowing method; Nekhoroshev's estimates},
language = {fre},
number = {2},
pages = {205-252},
publisher = {Gauthier-Villars},
title = {Transition le long des chaînes de tores invariants pour les systèmes hamiltoniens analytiques},
url = {http://eudml.org/doc/76713},
volume = {64},
year = {1996},
}

TY - JOUR
AU - Marco, Jean-Pierre
TI - Transition le long des chaînes de tores invariants pour les systèmes hamiltoniens analytiques
JO - Annales de l'I.H.P. Physique théorique
PY - 1996
PB - Gauthier-Villars
VL - 64
IS - 2
SP - 205
EP - 252
LA - fre
KW - lambda-lemma; existence of orbits; extremal tori; normal form; transition time; Easton's windowing method; Nekhoroshev's estimates
UR - http://eudml.org/doc/76713
ER -

References

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  1. [1] V.M. Alexeiev, Quasirandom dynamical systems, Math. USSR Sbornik, Vol. 68, 1968, p. 73-128. Zbl0198.56903
  2. [2] V.I. Arnold, Instability of dynamical systems with several degrees of freedom, Dokl. Acad. Nauk. SSSR, Vol. 156, 1964, p. 9-11. Zbl0135.42602MR163026
  3. [3] V.I. Arnold, Mathematical problems in classical physics, Appl. Math. Sc. Series, Vol. 100, 1992, p. 1-14. Zbl0806.53078MR1277190
  4. [4] P. Bernard, Note aux C.R.A.S., en préparation. 
  5. [5] U. Bessi, An approach to Arnold diffusion through the Calculus of Variations, Preprint. 
  6. [6] L. Chierchia et G. Gallavotti, Drift and diffusion in phase space, Annales de l'IHP, Physique Théorique, Vol. 60, 1994, p. 1-144. Zbl1010.37039MR1259103
  7. [7] A. Delshams Valdés, Por qué la diffusión de Arnold aparece genéricamente en los sistemas con màs de 3 grados de libertad, Thèse, Université de Barcelone, 1986. 
  8. [8] R. Douady, Stabilité ou instabilité des points fixes elliptiques, Annal. Sci. de l'E.N.S., Vol. 21, 1988, p. 1-46. Zbl0656.58020MR944100
  9. [9] H.S. Dumas, Ergodization rates for linear flows on the torus, Journal of Dynamics and Diff. Eq., Vol. 3, 1991, p. 593-610. Zbl0745.58032MR1129562
  10. [10] R. Easton, Orbit structure near trajectories biasymptotic to invariant tori, Classical Mechanics and Dynamical Systems, Marcel Dekker, 1981, p. 55-67. Zbl0502.70024MR640118
  11. [11] S. Graff, On the conservation of hyperbolic invariant tori for hamiltonian systems, Journal of Diff. Eq., Vol. 15, 1974, p. 1-69. Zbl0257.34048MR365626
  12. [12] C. Jones et N. Kopell, Tracking invariant manifolds with differential forms, à paraître dans Journal of Diff. Eq., 1994. Zbl0796.34038
  13. [13] P. Lochak, Canonical perturbation theory via simultaneous approximation, Russian Math. Surveys, Vol. 47, 1992, p. 57-133. Zbl0795.58042MR1209145
  14. [14] P. Lochak, Arnold diffusion; a compendium of remarks and questions, Preprint, 1994. Zbl0986.37054MR1720892
  15. [15] J. Mather, Variational construction of connecting orbits, Ann. Inst. Fourier, Vol. 43, 1993, p. 1349-1386. Zbl0803.58019MR1275203
  16. [16] H. Poincaré, Divergence des séries (parag. 225), Les méthodes nouvelles de la Mécanique Céleste, Blanchard1987. Zbl0651.70002
  17. [17] D. Sauzin, Résurgence paramétrique et petitesse exponentielle de l'écart des séparatrices dans le pendule rapidement forcé, Thèse, Université Paris VII, 1994. 
  18. [18] D.V. Treshchev, The mechanism of destruction of resonance tori of hamiltonian systems, Math. USSR Sbornik, Vol. 68, 1991, p. 181-203. Zbl0737.58025MR1025685

Citations in EuDML Documents

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  1. Massimiliano Berti, Philippe Bolle, Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems
  2. Pierre Lochak, Jean-Pierre Marco, Diffusion times and stability exponents for nearly integrable analytic systems
  3. Massimiliano Berti, Luca Biasco, Philippe Bolle, Optimal stability and instability results for a class of nearly integrable Hamiltonian systems
  4. Massimiliano Berti, Philippe Bolle, A functional analysis approach to Arnold diffusion

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