@article{ASENS_1993_4_26_5_545_0, author = {Gavrilov, Ljubomir and Ouazzani-Jamil, Mohammed and Caboz, R\'egis}, title = {Bifurcation diagrams and {Fomenko{\textquoteright}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}, pages = {545--564}, publisher = {Elsevier}, volume = {Ser. 4, 26}, number = {5}, year = {1993}, doi = {10.24033/asens.1680}, mrnumber = {94i:70017}, zbl = {0797.34042}, language = {en}, url = {http://www.numdam.org/articles/10.24033/asens.1680/} }
TY - JOUR AU - Gavrilov, Ljubomir AU - Ouazzani-Jamil, Mohammed AU - Caboz, Régis TI - Bifurcation diagrams and Fomenko’s surgery on Liouville tori of the Kolossoff potential $U=\rho +(1/\rho )-k\cos \phi $ JO - Annales scientifiques de l'École Normale Supérieure PY - 1993 SP - 545 EP - 564 VL - 26 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.24033/asens.1680/ DO - 10.24033/asens.1680 LA - en ID - ASENS_1993_4_26_5_545_0 ER -
%0 Journal Article %A Gavrilov, Ljubomir %A Ouazzani-Jamil, Mohammed %A Caboz, Régis %T Bifurcation diagrams and Fomenko’s surgery on Liouville tori of the Kolossoff potential $U=\rho +(1/\rho )-k\cos \phi $ %J Annales scientifiques de l'École Normale Supérieure %D 1993 %P 545-564 %V 26 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.24033/asens.1680/ %R 10.24033/asens.1680 %G en %F 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, Série 4, Tome 26 (1993) no. 5, pp. 545-564. doi : 10.24033/asens.1680. http://www.numdam.org/articles/10.24033/asens.1680/
[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 | Zbl
,[3] Integrability and Nonintegrability in Geometry and Mechanics, Kluwer Acad. Publishers, 1988. | MR | Zbl
,[4] On the Geometry of Gorjatchev-Tchaplygin top (Compt. rend. Acad. bulg. Sci., Vol. 40, No 9, pp. 33-36, 1987). | MR | Zbl
,[5] Bifurcations of Invariant Manifolds in the Generalized Hénon-Heiles System (Physica D, Vol. 34, 1989, pp. 223-239). | MR | Zbl
,[6] Non-Integrability of the Equation of Heavy Gyrostat (Comp. Mathematica, Vol. 82, 1992, pp. 275-291). | Numdam | MR | Zbl
,[7] Principles of Algebraic Geometry, Wiley-Interscience, New York, 1978. | MR | Zbl
and ,[8] Zur Rotation eines Körpers im Kowalewski'schen Falle, (Mathematische Annalen, Vol. 56, 1903, pp. 265-272). | JFM
,[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 | Zbl
,[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 | Zbl
,[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 | MR
,[12] Klein Surfaces (Russian Math. Surveys, Vol. 45, 6, 1990, pp. 53-108). | MR | Zbl
,[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 | Zbl
and ,[14] Encyklopädie der Mathematischen Wissenschaften, Band II, 2 Teil (Leipzig 1901), pp. 766-768.
[15] Zbl
(Celestial Mech., Vol. 31, 1983, p. 363). |Cité par Sources :