The four positive vortices problem : regions of chaotic behavior and the non-integrability

M. S. A. C. Castilla; Vinicio Moauro; Piero Negrini; Waldyr Muniz Oliva

Annales de l'I.H.P. Physique théorique (1993)

  • Volume: 59, Issue: 1, page 99-115
  • ISSN: 0246-0211

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Castilla, M. S. A. C., et al. "The four positive vortices problem : regions of chaotic behavior and the non-integrability." Annales de l'I.H.P. Physique théorique 59.1 (1993): 99-115. <http://eudml.org/doc/76617>.

@article{Castilla1993,
author = {Castilla, M. S. A. C., Moauro, Vinicio, Negrini, Piero, Oliva, Waldyr Muniz},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {perturbation; planar autonomous Hamiltonian system; saddle connections; periodically time-dependent Hamiltonian system},
language = {eng},
number = {1},
pages = {99-115},
publisher = {Gauthier-Villars},
title = {The four positive vortices problem : regions of chaotic behavior and the non-integrability},
url = {http://eudml.org/doc/76617},
volume = {59},
year = {1993},
}

TY - JOUR
AU - Castilla, M. S. A. C.
AU - Moauro, Vinicio
AU - Negrini, Piero
AU - Oliva, Waldyr Muniz
TI - The four positive vortices problem : regions of chaotic behavior and the non-integrability
JO - Annales de l'I.H.P. Physique théorique
PY - 1993
PB - Gauthier-Villars
VL - 59
IS - 1
SP - 99
EP - 115
LA - eng
KW - perturbation; planar autonomous Hamiltonian system; saddle connections; periodically time-dependent Hamiltonian system
UR - http://eudml.org/doc/76617
ER -

References

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  2. [C-M] A.J. Chorin and J.E. Marsden, A Mathematical Introduction to Fluid Mechanics, Springer Verlag, 1979. Zbl0417.76002MR551053
  3. [H] P.J. Holmes, Averaging and Chaotic Motions in Forced Oscillations, S.I.A.M. J. Appl. Math., Vol. 38, 1, 1980, pp. 65-79. Errata, Vol. 40, 1, 1981, pp. 167-168. Zbl0472.70024MR559081
  4. [K] K.M. Khanin, Quasi-Periodic Motions on Vortex Systems, Physics, Vol. 4D, 1982, pp. 261-269. Zbl1194.76028MR653779
  5. [K-C] J. Koiller and S. Carvalho, Non-Integrability of the 4-Vortex System, Analytical Proof, Comm. Math. Phys., Vol. 120, 1989, pp. 643-652. Zbl0825.58013MR987772
  6. [M-C] C. Marchioro and M. Pulvirenti, Vortex Methods in Two Dimensional Fluid Dynamics, Edizioni Klim, Roma, 1983. Zbl0545.76027MR750980
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  8. [Mo] J. Moser, Stable and Random Motions in Dynamical Systems, Princeton Univ. Press, Princeton N.J., Univ. of Tokyo Press, Tokyo, 1973. MR442980
  9. [O1] W.M. Oliva, Integrability Problems in Hamiltonian Systems, Ravello (Italy), XVI Summer School on Mathematical Physics, 1991. 
  10. [O2] W.M. Oliva, On the chaotic behaviour and non integrability of the four vortices problems, Ann. Inst. H. Poincaré, Vol. 55, 21, 1991, pp. 707-718. Zbl0738.76008MR1139542
  11. [S] S. Smale, The Mathematics of Time. Essays on Dynamical Systems. Economic Process and Related Topics, Springer-Verlag, 1980. Zbl0451.58001MR607330
  12. [Sy] J.L. Synge, On the Motion of Three Vortices, Can. Journal of Math., Vol. 1, 1949, pp. 257-270. Zbl0032.22303MR30841
  13. [Z] S.L. Ziglin, Non Integrability of a Problem on the Motion of Four Point Vortices, Soviet. Math. Dokl., Vol. 21, 1, 1980, pp. 296-299. Zbl0464.76021

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