@article{ASENS_1993_4_26_5_545_0, author = {Gavrilov, Lubomir and Ouazzani-Jamil, Mohammed and Caboz, R\'egis}, title = {Bifurcation diagrams and Fomenko's surgery on Liouville tori of the Kolossoff potential $U=\rho +(1/\rho )-k\cos \phi $}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, volume = {26}, year = {1993}, pages = {545-564}, doi = {10.24033/asens.1680}, mrnumber = {94i:70017}, zbl = {0797.34042}, language = {en}, url = {http://dml.mathdoc.fr/item/ASENS_1993_4_26_5_545_0} }
Gavrilov, Ljubomir; Ouazzani-Jamil, Mohammed; Caboz, Régis. Bifurcation diagrams and Fomenko’s surgery on Liouville tori of the Kolossoff potential $U=\rho +(1/\rho )-k\cos \phi $. Annales scientifiques de l'École Normale Supérieure, Tome 26 (1993) pp. 545-564. doi : 10.24033/asens.1680. http://gdmltest.u-ga.fr/item/ASENS_1993_4_26_5_545_0/
[1] Algebraic Completely Integrable Systems : a systematic approach, Perspectives in Mathematics, Academic Press (to appear in 1992).
and ,[2] Solution of Equations of Problm of Motion of a Heavy Rigid Body About a Fixed Point in the Kowalevskaya's Case Using θ - Function (Celestial Mech., Vol. 29, 1983, pp. 249-253.). | MR 84e:70004 | Zbl 0513.70008
,[3] Integrability and Nonintegrability in Geometry and Mechanics, Kluwer Acad. Publishers, 1988. | MR 90c:58054 | Zbl 0675.58018
,[4] On the Geometry of Gorjatchev-Tchaplygin top (Compt. rend. Acad. bulg. Sci., Vol. 40, No 9, pp. 33-36, 1987). | MR 89b:58091 | Zbl 0632.58021
,[5] Bifurcations of Invariant Manifolds in the Generalized Hénon-Heiles System (Physica D, Vol. 34, 1989, pp. 223-239). | MR 90h:58040 | Zbl 0689.58014
,[6] Non-Integrability of the Equation of Heavy Gyrostat (Comp. Mathematica, Vol. 82, 1992, pp. 275-291). | Numdam | MR 93d:70008 | Zbl 0748.70003
,[7] Principles of Algebraic Geometry, Wiley-Interscience, New York, 1978. | MR 80b:14001 | Zbl 0408.14001
and ,[8] Zur Rotation eines Körpers im Kowalewski'schen Falle, (Mathematische Annalen, Vol. 56, 1903, pp. 265-272). | JFM 33.0762.01
,[9] Bifurcation of Common Levels of First Integrals of the Kovalevskaya Problem (PMM U.S.S.R., Vol. 47, No 6, 1983, pp. 737-743). | MR 86h:70005 | Zbl 0579.70003
,[10] Topological Analysis of Classical Integrable Systems in the Dynamics of the Rigid Body (Soviet Math. Dokl., Vol. 28, No 3, 1983, pp. 802-805). | MR 86c:70003 | Zbl 0561.58021
,[11] Sur le problème de la rotation d'un corps solide autour d'un point fixe (Acta Math., Vol. 12, 1889, pp. 177-232). | JFM 21.0935.01 | MR 1916790
,[12] Klein Surfaces (Russian Math. Surveys, Vol. 45, 6, 1990, pp. 53-108). | MR 92i:14029 | Zbl 0734.30037
,[13] Topological classification of integrable non-degenerate Hamiltonians on a constant energy three-dimensional sphere (Russian Math. Surveys, Vol. 45, 6, 1990, pp. 109-135). | MR 92h:58088 | Zbl 0721.58022
and ,[14] Encyklopädie der Mathematischen Wissenschaften, Band II, 2 Teil (Leipzig 1901), pp. 766-768.
[15] | Zbl 0556.70014
(Celestial Mech., Vol. 31, 1983, p. 363).