Bifurcation diagrams and Fomenko’s surgery on Liouville tori of the Kolossoff potential U = ρ + ( 1 / ρ ) - k cos φ

Ljubomir Gavrilov; Mohammed Ouazzani-Jamil; Régis Caboz

Annales scientifiques de l'École Normale Supérieure (1993)

  • Volume: 26, Issue: 5, page 545-564
  • ISSN: 0012-9593

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Gavrilov, Ljubomir, Ouazzani-Jamil, Mohammed, and 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 26.5 (1993): 545-564. <http://eudml.org/doc/82349>.

@article{Gavrilov1993,
author = {Gavrilov, Ljubomir, Ouazzani-Jamil, Mohammed, Caboz, Régis},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {motion of a particle; potential field; Hamiltonian system; topology; bifurcations; invariant level sets},
language = {eng},
number = {5},
pages = {545-564},
publisher = {Elsevier},
title = {Bifurcation diagrams and Fomenko’s surgery on Liouville tori of the Kolossoff potential $U=\rho +(1/\rho )-k\cos \phi $},
url = {http://eudml.org/doc/82349},
volume = {26},
year = {1993},
}

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
PB - Elsevier
VL - 26
IS - 5
SP - 545
EP - 564
LA - eng
KW - motion of a particle; potential field; Hamiltonian system; topology; bifurcations; invariant level sets
UR - http://eudml.org/doc/82349
ER -

References

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  2. [2] F. M. El-SABAA, 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.). Zbl0513.70008MR84e:70004
  3. [3] A. T. FOMENKO, Integrability and Nonintegrability in Geometry and Mechanics, Kluwer Acad. Publishers, 1988. Zbl0675.58018MR90c:58054
  4. [4] L. GAVRILOV, On the Geometry of Gorjatchev-Tchaplygin top (Compt. rend. Acad. bulg. Sci., Vol. 40, No 9, pp. 33-36, 1987). Zbl0632.58021MR89b:58091
  5. [5] L. GAVRILOV, Bifurcations of Invariant Manifolds in the Generalized Hénon-Heiles System (Physica D, Vol. 34, 1989, pp. 223-239). Zbl0689.58014MR90h:58040
  6. [6] L. GAVRILOV, Non-Integrability of the Equation of Heavy Gyrostat (Comp. Mathematica, Vol. 82, 1992, pp. 275-291). Zbl0748.70003MR93d:70008
  7. [7] P. GRIFFITHS and J. HARRIS, Principles of Algebraic Geometry, Wiley-Interscience, New York, 1978. Zbl0408.14001MR80b:14001
  8. [8] G. KOLOSSOFF, Zur Rotation eines Körpers im Kowalewski'schen Falle, (Mathematische Annalen, Vol. 56, 1903, pp. 265-272). Zbl33.0762.01JFM33.0762.01
  9. [9] M. P. KHARLAMOV, Bifurcation of Common Levels of First Integrals of the Kovalevskaya Problem (PMM U.S.S.R., Vol. 47, No 6, 1983, pp. 737-743). Zbl0579.70003MR86h:70005
  10. [10] M. P. KHARLAMOV, Topological Analysis of Classical Integrable Systems in the Dynamics of the Rigid Body (Soviet Math. Dokl., Vol. 28, No 3, 1983, pp. 802-805). Zbl0561.58021MR86c:70003
  11. [11] S. KOVALEVSKAYA, Sur le problème de la rotation d'un corps solide autour d'un point fixe (Acta Math., Vol. 12, 1889, pp. 177-232). MR1916790JFM21.0935.01
  12. [12] S. M. NATANZON, Klein Surfaces (Russian Math. Surveys, Vol. 45, 6, 1990, pp. 53-108). Zbl0734.30037MR92i:14029
  13. [13] NGUEN T'EN ZUNG and A. T. FOMENKO, Topological classification of integrable non-degenerate Hamiltonians on a constant energy three-dimensional sphere (Russian Math. Surveys, Vol. 45, 6, 1990, pp. 109-135). Zbl0721.58022MR92h:58088
  14. [14] Encyklopädie der Mathematischen Wissenschaften, Band II, 2 Teil (Leipzig 1901), pp. 766-768. 
  15. [15] H. YOSHIDA (Celestial Mech., Vol. 31, 1983, p. 363). Zbl0556.70014

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