@article{CM_1996__101_2_179_0, author = {Zung, Nguyen Tien}, title = {Symplectic topology of integrable hamiltonian systems, {I} : {Arnold-Liouville} with singularities}, journal = {Compositio Mathematica}, pages = {179--215}, publisher = {Kluwer Academic Publishers}, volume = {101}, number = {2}, year = {1996}, mrnumber = {1389366}, zbl = {0936.37042}, language = {en}, url = {http://archive.numdam.org/item/CM_1996__101_2_179_0/} }
TY - JOUR AU - Zung, Nguyen Tien TI - Symplectic topology of integrable hamiltonian systems, I : Arnold-Liouville with singularities JO - Compositio Mathematica PY - 1996 SP - 179 EP - 215 VL - 101 IS - 2 PB - Kluwer Academic Publishers UR - http://archive.numdam.org/item/CM_1996__101_2_179_0/ LA - en ID - CM_1996__101_2_179_0 ER -
%0 Journal Article %A Zung, Nguyen Tien %T Symplectic topology of integrable hamiltonian systems, I : Arnold-Liouville with singularities %J Compositio Mathematica %D 1996 %P 179-215 %V 101 %N 2 %I Kluwer Academic Publishers %U http://archive.numdam.org/item/CM_1996__101_2_179_0/ %G en %F CM_1996__101_2_179_0
Zung, Nguyen Tien. Symplectic topology of integrable hamiltonian systems, I : Arnold-Liouville with singularities. Compositio Mathematica, Volume 101 (1996) no. 2, pp. 179-215. http://archive.numdam.org/item/CM_1996__101_2_179_0/
1 Mathematical methods of classical mechanics, Springer-Verlag, 1978. | MR | Zbl
:2 The topology of torus action on symplectic manifolds, Progress in Mathematics, V. 93, Birkhauser, 1991. | MR | Zbl
:3 Courbes algébriques et systèmes intégrables: géodésiques des quadriques, preprint IRMA Strasbourg 1993. | MR | Zbl
:4 Toupies, A course on integrable systems, Strasbourg 1994.
:5 Variétés abéliennes réelles et toupie de Kowalevski, Compositio Math. 87 (1993), 153-229. | Numdam | MR | Zbl
and :6 Monodromy in the champagne bottle, Z. Angew. Math. Phys. 42 (1991) No. 6, 837-847. | MR | Zbl
:7 Separation of coordinates and topology of integrable Hamiltonian systems, in preparation.
and :8 Dynamical systems, AMS Colloq. Publ. IX, 1927.
:9 Methods of computation of the Fomenko-Zieschang invariant, Advances in Soviet Mathematics, V. 6 (Fomenko ed.), 1991, 147-183. | MR | Zbl
:10 Compatible Poisson brackets on Lie algebras and completeness of families of functions in involution, Math. USSR Izvestiya 38 (1992) 69-90. | MR | Zbl
:11 Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of all systems of small complexity, Russ. Math. Surv. 45 (1990) No. 2, 59-99. | MR | Zbl
, and :12 Géométrie globale des systèmes hamiltoniens complètement integrables, CRAS Paris, Ser. I, 308 (1989) 421-424. | MR | Zbl
and :13 Géométrie du moment, Séminaire Sud-Phodanien, Publications du départment de math., Univ. Claude Bernard - Lion I, 1988. | MR
, and :14 The energy momentum mapping of the Lagrange top, Lecture Notes in Math. 1139 (1985) 12-24. | MR | Zbl
and :15 Le problème général des variables action-angles, J. Diff. Geom. 26 (1987) No. 2, 223-251. | MR | Zbl
and :16 Hamiltoniens périodiques et image convexe de l'application moment, Bull. Soc. Math. France 116 (1988) 315-339. | Numdam | MR | Zbl
:17 Singular Lagrangian foliation associated to an integrable Hamiltonian vector field, MSRI Publ., Vol. 20 (1990) 129-136. | MR | Zbl
:18 Transversal homoclinic orbit in an integrable system, Amer. J. Math. 100 (1978) 631-642. | MR | Zbl
:19 Théorème de Nekhoroshev à singularités, Séminaire Gaston Darboux, Montpellier 1989- 1990, 49-56. | MR | Zbl
:20 Compactification d'action de Rn et variables action-angle avec singularités, MSRI Publ., Vol. 20 (1990) (Séminaire Sud-Rhodanien de Géométrie à Berkeley, 1989, P. Dazord and A. Weinstein eds.) 151-167 | MR | Zbl
and :21 On global action-angle variables, Comm. Pure Appl. Math. 33 (1980) 687-706. | MR | Zbl
:22 On the variation in the cohomology of the symplectic form of the reduced phase space and Addendum, Invent. Math. 69 (1982) 259-269 and 72 (1983) 153-158. | MR | Zbl
and :23 Normal form for Hamiltonian systems with Poisson commuting integrals- elliptic case, Comm. Math. Helv. 65 (1990) 4-35. | Zbl
:24 Towarda topological classification of integrable PDE's, MSRI Publ., V. 22 (1990) 111-130. | Zbl
and :25 Symplectic geometry, Gordon and Breach, New York, 1988, and Integrability and nonintegrability in geometry and mechanics, Kluwer, Dordrecht, 1988. | MR
:26 Topological classification of all integrable Hamiltonian systems of general types with two degrees of freedom, MSRI Publ., Vol. 22 (1991) 131-340. | MR | Zbl
:27 Bifurcation of invariant manifolds in the generalized Hénon-Heiles system, Physica D, 34 (1989) 223-239. | MR | Zbl
:28 Bifurcation diagrams and Fomenko's surgery on Liouville tori of the Kolossoff potential U = p + (1/ρ) - k cos Φ, Ann. Sci. Ecole Norm. Sup., 4e serie, 26 (1993) 545-564. | Numdam | Zbl
, and :29 Topological analysis of integrable problems in the dynamics of a rigid body, Izd. Leningrad. Univ., Leningrad (Saint-Peterbourg) 1988 (Russian). | MR
:30 Melnikov formulae for nearly integrable Hamiltonian systems, MSRI Publ., V. 20 (1990) 183-188. | MR | Zbl
:31 Sur le problème de la rotation d'un corps solide autour d'un point fixe, Acta Math. 12 (1989) 177-232. | JFM
:32 Structure of the Poisson action of R 2 on a four-dimensional symplectic manifold, I and II, Selecta Math. Sovietica Vol. 6, No. 4 (1987) 365-396, and Vol. 7, No. 1 (1988) 39-48. | MR | Zbl
and :33 Classification of four-dimensional integrable Hamiltonian systems in extended neighborhoods of simple singular points, Methods of Qualitative Theory of Bifurcations, Izdat. Gorkov. Univ., Gorki, 1988, 67-76.
and :34 Classification of four-dimensional integrable hamiltonian systems and Poisson actions of R2 in extended neighborhoods of simple singular points, I and II, Russian Math. Sb. 77 (1994) 511-542 and 78 (1994) 479-506. | MR | Zbl
and :35 Reduction of symplectic manifolds with symmetry, Rep. Math. Phys. 5 (1974) 121-130. | MR | Zbl
and :36 On the volume elements on manifolds, Trans. AMS 120 (1965) 280-296. | MR | Zbl
:37 Du théorème d'Arnol'd-Liouville aux formes normales de systmèmes hamiltoniens toriques: une conjecture. Séminaire Gaston Darboux, Montpellier 1989-1990, 39-47. | MR | Zbl
:38 Action-angle variables and their generalizations, Trans. Moscow Math. Soc. 26 (1972) 180-198. | MR | Zbl
:39 Fomenko invariants for the main integrable cases of the rigid body motion equations, Advances in Soviet Mathematics, V. 6 (1991) A. T. Fomenko ed., 67-146. | MR | Zbl
:40 A topological classification of integrable geodesic flows on the two-dimensional sphere with an additional integral quadratic in the momenta, J. Nonlinear Sci. 3 (1993) No.1, 85-108. | MR | Zbl
and :41 Über das Verhalten analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung, Math. Ann. 154 (1964) 285-300. | MR | Zbl
:42 Compactification d'actions de Rn et systèmes hamiltoniens de type torique, CRAS Paris, Ser. I 317 (1993) 289-293. | MR | Zbl
:43 Sur certaines systèmes dynamiques séparables, Amer. J. Math. 100 (1978) 591-614. | MR | Zbl
:44 On the algebraic problem concerning the normal forms of linear dynamical systems, Amer. J. Math. 58:1 (1936) 141-163. | JFM | MR
:45 Monodromy in two degrees of freedom integrable systems, J. Geom. and Phys. 10 (1992) 37-45. | MR | Zbl
:46 On the general position property of simple Bott integrals, Russ. Math. Surv. 45 (1990) No. 4, 179-180. | MR | Zbl
:47 Nguyen: Decomposition of nondegenerate singularities of integrable Hamiltonian systems, Lett. Math. Phys. 33 (1994) 187-193. | MR | Zbl
,48 A note on focus-focus singularities, Diff. Geom. Appl. (to appear). | Zbl
:49 Symplectic topology of integrable Hamiltonian systems, thesis, Strasbourg May/1994.
:50 Singularities of integrable geodesic flows on multidimensional torus and sphere, J. Geometry and Physics (to appear). | MR | Zbl
:51 Symplectic topology of integrable Hamiltonian systems, II: Characteristic classes and integrable surgery, preprint 1995. | MR
: