@article{AIHPA_1993__59_1_99_0, author = {Castilla, M. S. A. C. and Moauro, Vinicio and Negrini, Piero and Oliva, Waldyr Muniz}, title = {The four positive vortices problem : regions of chaotic behavior and the non-integrability}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {99--115}, publisher = {Gauthier-Villars}, volume = {59}, number = {1}, year = {1993}, mrnumber = {1244184}, zbl = {0792.76010}, language = {en}, url = {http://archive.numdam.org/item/AIHPA_1993__59_1_99_0/} }
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 SP - 99 EP - 115 VL - 59 IS - 1 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPA_1993__59_1_99_0/ LA - en ID - AIHPA_1993__59_1_99_0 ER -
%0 Journal Article %A Castilla, M. S. A. C. %A Moauro, Vinicio %A Negrini, Piero %A Oliva, Waldyr Muniz %T The four positive vortices problem : regions of chaotic behavior and the non-integrability %J Annales de l'I.H.P. Physique théorique %D 1993 %P 99-115 %V 59 %N 1 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPA_1993__59_1_99_0/ %G en %F AIHPA_1993__59_1_99_0
Castilla, M. S. A. C.; Moauro, Vinicio; Negrini, Piero; Oliva, Waldyr Muniz. The four positive vortices problem : regions of chaotic behavior and the non-integrability. Annales de l'I.H.P. Physique théorique, Tome 59 (1993) no. 1, pp. 99-115. http://archive.numdam.org/item/AIHPA_1993__59_1_99_0/
[A - P] 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. | MR | Zbl
and ,[C-M] A Mathematical Introduction to Fluid Mechanics, Springer Verlag, 1979. | MR | Zbl
and ,[H] 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. | MR | Zbl
,[K] Quasi-Periodic Motions on Vortex Systems, Physics, Vol. 4D, 1982, pp. 261-269. | MR | Zbl
,[K-C] Non-Integrability of the 4-Vortex System, Analytical Proof, Comm. Math. Phys., Vol. 120, 1989, pp. 643-652. | MR | Zbl
and ,[M-C] Vortex Methods in Two Dimensional Fluid Dynamics, Edizioni Klim, Roma, 1983. | MR | Zbl
and ,[M] On the Stability of the Center for Time-Periodic Perturbations, Trans. Moscow Math. Soc., Vol. 12, 1, 1963, pp. 1-57. | MR | Zbl
,[Mo] Stable and Random Motions in Dynamical Systems, Princeton Univ. Press, Princeton N.J., Univ. of Tokyo Press, Tokyo, 1973. | MR | Zbl
,[O1] Integrability Problems in Hamiltonian Systems, Ravello (Italy), XVI Summer School on Mathematical Physics, 1991.
,[O2] On the chaotic behaviour and non integrability of the four vortices problems, Ann. Inst. H. Poincaré, Vol. 55, 21, 1991, pp. 707-718. | Numdam | MR | Zbl
,[S] The Mathematics of Time. Essays on Dynamical Systems. Economic Process and Related Topics, Springer-Verlag, 1980. | MR | Zbl
,[Sy] On the Motion of Three Vortices, Can. Journal of Math., Vol. 1, 1949, pp. 257-270. | MR | Zbl
,[Z] Non Integrability of a Problem on the Motion of Four Point Vortices, Soviet. Math. Dokl., Vol. 21, 1, 1980, pp. 296-299. | Zbl
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