The geometry of nondegeneracy conditions in completely integrable systems

Nicolas Roy

Annales de la Faculté des sciences de Toulouse : Mathématiques (2005)

  • Volume: 14, Issue: 4, page 705-719
  • ISSN: 0240-2963

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Roy, Nicolas. "The geometry of nondegeneracy conditions in completely integrable systems." Annales de la Faculté des sciences de Toulouse : Mathématiques 14.4 (2005): 705-719. <http://eudml.org/doc/73664>.

@article{Roy2005,
author = {Roy, Nicolas},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {KAM theorems; geometrical formulation; fibration of a symplectic manifold; Lagrangian tori; nondegenerate Hamiltonians},
language = {eng},
number = {4},
pages = {705-719},
publisher = {Université Paul Sabatier, Institut de Mathématiques},
title = {The geometry of nondegeneracy conditions in completely integrable systems},
url = {http://eudml.org/doc/73664},
volume = {14},
year = {2005},
}

TY - JOUR
AU - Roy, Nicolas
TI - The geometry of nondegeneracy conditions in completely integrable systems
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2005
PB - Université Paul Sabatier, Institut de Mathématiques
VL - 14
IS - 4
SP - 705
EP - 719
LA - eng
KW - KAM theorems; geometrical formulation; fibration of a symplectic manifold; Lagrangian tori; nondegenerate Hamiltonians
UR - http://eudml.org/doc/73664
ER -

References

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  1. [1] Arnol'd ( V.I.). — A theorem of Liouville concerning integrable dynamics, Siberizn Math. J.4, p. 471-474 (1963). Zbl0189.24401MR147742
  2. [2] Bruno ( A.D. ). — Local Methods in nonlinear differential equations , Springer-Verlag (1989). Zbl0674.34002MR993771
  3. [3] Dixmier ( J. ). — Topologie Générale, Presses Universitaires de France (1981). Zbl0449.54001MR637202
  4. [4] Duistermaat ( J.J.). — Global action-angle coordinates , Comm. Pure App. Math.32, p. 687-706 (1980). Zbl0439.58014MR596430
  5. [5] Kolmogorov ( A.N.). — On conservation of conditionally periodic motions for a small change in Hamilton's function, Dokl. Akad. Nauk. SSSR, 98(4) p. 527-530 (1954). Zbl0056.31502MR68687
  6. [6] Liouville ( J.).— Note sur l'intégration des équations différentielles de la dynamique, J. Math. Pure App.20, p. 137-138 (1855). 
  7. [7] Mineur ( H. ). — Réduction des systèmes mécaniques à n degrés de libertés admettant n intégrales premières uniformes en involution aux systèmes à variables séparées, J. Math. Pure Appl.15, p. 221-267 (1936). Zbl0015.32401JFM62.1513.02
  8. [8] Rüssmann ( H.). — Nondegeneracy in the perturbation theory of integrable dynamical systems. In Number theory and dynamical systems (York, 1987), volume 134 of London Math. Soc. Lecture Note Ser., p. 5-18. Cambridge Univ. Press, Cambridge (1989). Zbl0689.34039
  9. [9] Weinstein ( A.). — Symplectic manifolds and their lagrangian subamnifolds, Adv. in Math.6, 329-346 (1971). Zbl0213.48203MR286137
  10. [10] Weinstein ( A.). — Lagrangian submanifolds and hamiltonian systems, Ann. of Math.98, p. 377-410 (1973). Zbl0271.58008MR331428

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