@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}, volume = {59}, year = {1993}, pages = {99-115}, mrnumber = {1244184}, zbl = {0792.76010}, language = {en}, url = {http://dml.mathdoc.fr/item/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) pp. 99-115. http://gdmltest.u-ga.fr/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 660416 | Zbl 0483.76031
and ,[C-M] A Mathematical Introduction to Fluid Mechanics, Springer Verlag, 1979. | MR 551053 | Zbl 0417.76002
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 559081 | Zbl 0518.70023 | Zbl 0472.70024
,[K] Quasi-Periodic Motions on Vortex Systems, Physics, Vol. 4D, 1982, pp. 261-269. | MR 653779 | Zbl 1194.76028
,[K-C] Non-Integrability of the 4-Vortex System, Analytical Proof, Comm. Math. Phys., Vol. 120, 1989, pp. 643-652. | MR 987772 | Zbl 0825.58013
and ,[M-C] Vortex Methods in Two Dimensional Fluid Dynamics, Edizioni Klim, Roma, 1983. | MR 750980 | Zbl 0545.76027
and ,[M] On the Stability of the Center for Time-Periodic Perturbations, Trans. Moscow Math. Soc., Vol. 12, 1, 1963, pp. 1-57. | MR 156048 | Zbl 0135.31001
,[Mo] Stable and Random Motions in Dynamical Systems, Princeton Univ. Press, Princeton N.J., Univ. of Tokyo Press, Tokyo, 1973. | MR 442980 | Zbl 0271.70009
,[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 1139542 | Zbl 0738.76008
,[S] The Mathematics of Time. Essays on Dynamical Systems. Economic Process and Related Topics, Springer-Verlag, 1980. | MR 607330 | Zbl 0451.58001
,[Sy] On the Motion of Three Vortices, Can. Journal of Math., Vol. 1, 1949, pp. 257-270. | MR 30841 | Zbl 0032.22303
,[Z] Non Integrability of a Problem on the Motion of Four Point Vortices, Soviet. Math. Dokl., Vol. 21, 1, 1980, pp. 296-299. | Zbl 0464.76021
,