On the chaotic behavior and the non-integrability of the four vortices problem

W. M. Oliva

Annales de l'I.H.P. Physique théorique (1991)

  • Volume: 55, Issue: 2, page 707-718
  • ISSN: 0246-0211

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Oliva, W. M.. "On the chaotic behavior and the non-integrability of the four vortices problem." Annales de l'I.H.P. Physique théorique 55.2 (1991): 707-718. <http://eudml.org/doc/76549>.

@article{Oliva1991,
author = {Oliva, W. M.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {chaotic behavior; non-integrability; quasi-periodicity; vortex motions; four points vortices},
language = {eng},
number = {2},
pages = {707-718},
publisher = {Gauthier-Villars},
title = {On the chaotic behavior and the non-integrability of the four vortices problem},
url = {http://eudml.org/doc/76549},
volume = {55},
year = {1991},
}

TY - JOUR
AU - Oliva, W. M.
TI - On the chaotic behavior and the non-integrability of the four vortices problem
JO - Annales de l'I.H.P. Physique théorique
PY - 1991
PB - Gauthier-Villars
VL - 55
IS - 2
SP - 707
EP - 718
LA - eng
KW - chaotic behavior; non-integrability; quasi-periodicity; vortex motions; four points vortices
UR - http://eudml.org/doc/76549
ER -

References

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  1. H. Aref and N. Pomphrey, Integrable and Chaotic Motions of Four Vortices. I. The Case of Identical Vortices, Proc. R. Soc. London Ser. A, Vol. 380, 1982, pp. 359-387. Zbl0483.76031MR660416
  2. H. Aref, Integrable, Chaotic and Turbulent Vortex Motion in Two-Dimensional flows, Ann. Rev. Fluid Mech., Vol. 15, 1983, pp. 345-389. Zbl0562.76029MR686292
  3. A.J. Chorin and J.E. Marsden, A Mathematical Introduction to Fluid Mechanics, Springer-Verlag, 1979. Zbl0417.76002MR551053
  4. D. Dürr and M. Pulvirenti, On the Vortex Flow in Bounded Domain, Commun. Math. Phys., Vol. 85, 1982, pp. 265-273. Zbl0503.60069MR676001
  5. 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
  6. P.J. Holmes and J.E. Marsden, Horseshoes in Perturbations of Hamiltonian System with Two Degrees of Freedom, Commun. Math. Phys., Vol. 82, 1982, pp. 523-544. Zbl0489.58013MR641913
  7. K.M. Khanin, Quasi-Periodic Motions of Vortex Systems, Physica, Vol. 4D, 1982, pp. 261- 269. Zbl1194.76028MR653779
  8. V.V. Kozlov, Integrability and Non-Integrability in Hamiltonian Mechanics, Russian Math. Surveys, Vol. 38.1, 1983, pp. 1-76. Zbl0525.70023MR693718
  9. C. Marchioro and M. Pulvirenti, Vortex Methods in Two Dimensional Fluid Dynamics, Edizioni Klim, Roma, 1983. Zbl0545.76027MR750980
  10. V.K. Melnikov, On the Stability of the Center of Time-Periodic Perturbations, Trans. Moscow Math. Soc., Vol. 12, (1), 1963, pp. 1-57. Zbl0135.31001MR156048
  11. J. Moser, Stable and Random Motions in Dynamical Systems, Princeton Univ. Press, Princeton N.J., Univ. of Tokyo Press, Tokyo, 1973. Zbl0271.70009MR442980
  12. S. Smale, The Mathematics of Time. Essays on Dynamical Systems, Economic Process, and Related Topics, Springer-Verlag, 1980. Zbl0451.58001MR607330
  13. S.L. Ziglin, Nonintegrability of a Problem on the Motion of Four Point Vortices, Soviet Math. Dokl., Vol. 21, No. 1, 1980, pp. 296-299. Zbl0464.76021

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