The geometry of nondegeneracy conditions in completely integrable systems
Annales de la Faculté des sciences de Toulouse : Mathématiques (2005)
- Volume: 14, Issue: 4, page 705-719
- ISSN: 0240-2963
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top- [1] Arnol'd ( V.I.). — A theorem of Liouville concerning integrable dynamics, Siberizn Math. J.4, p. 471-474 (1963). Zbl0189.24401MR147742
- [2] Bruno ( A.D. ). — Local Methods in nonlinear differential equations , Springer-Verlag (1989). Zbl0674.34002MR993771
- [3] Dixmier ( J. ). — Topologie Générale, Presses Universitaires de France (1981). Zbl0449.54001MR637202
- [4] Duistermaat ( J.J.). — Global action-angle coordinates , Comm. Pure App. Math.32, p. 687-706 (1980). Zbl0439.58014MR596430
- [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] Liouville ( J.).— Note sur l'intégration des équations différentielles de la dynamique, J. Math. Pure App.20, p. 137-138 (1855).
- [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] 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] Weinstein ( A.). — Symplectic manifolds and their lagrangian subamnifolds, Adv. in Math.6, 329-346 (1971). Zbl0213.48203MR286137
- [10] Weinstein ( A.). — Lagrangian submanifolds and hamiltonian systems, Ann. of Math.98, p. 377-410 (1973). Zbl0271.58008MR331428