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JOURNALS // Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki

Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, Issue 1, Pages 127–132 (Mi vuu180)

Numerical integration of differential dynamical equations. Vortex dynamics applications
A. V. Borisov

References

1. Bogomolov V. A., “Dinamika zavikhrennosti na sfere”, Izv. AN. SSSR. Mekh. zhid. i gaza, 1977, no. 6, 57–65  mathscinet  zmath
2. Borisov A. V., Mamaev I. S., “Matematicheskie metody dinamiki vikhrevykh struktur”, V sb. Fundamentalnye i prikladnye problemy teorii vikhrei, eds. Borisov A. V., Mamaev I. S., Sokolovskii M. A., NITs RKhD, 2003, 704 pp.
3. Borisov A. V., Mamaev I. S., Puassonovy struktury i algebry Li v gamiltonovoi mekhanike, Izd. dom. “Udmurtskii universitet”, Izhevsk, 1999, 464 pp.  mathscinet  zmath
4. Ziglin S. L., “Neintegriruemost zadachi o dvizhenie chetyrekh tochechnykh vikhrei”, DAN SSSR, 250:6 (1979), 1296–1300  mathnet  mathscinet
5. Kozlov V. V., Simmetrii, topologiya i rezonansy v gamiltonovoi mekhanike, Izd-vo UdGU, Izhevsk, 1995  mathscinet  zmath
6. Uintner A., Analiticheskie osnovy nebesnoi mekhaniki, Nauka, M., 1967
7. Sharle K. L., Nebesnaya mekhanika, Nauka, M., 1966, 627 pp.  mathscinet
8. Aref H., Pomphrey N., “Integrable and chaotic motions of four vortices. I. The case of identical vortices”, Proc. R. Soc. London A, 380 (1982), 359–387  crossref  mathscinet  zmath  adsnasa
9. Bolsinov A. V., Borisov A. V., Mamaev I. S., “Lie algebras in vortex dynamics and celestial mechanics IV”, Reg. & Chaot. Dyn., 4:1 (1999), 23–50  crossref  mathscinet  zmath
10. Eckhardt B., “Integrable four vortex motion”, Phys. Fluids, 31:10 (1988), 2796–2801  crossref  mathscinet  zmath  adsnasa  isi
11. Khanin K. M., “Quasi-periodic motions of vortex systems”, Physica D, 4 (1982), 261–269  crossref  mathscinet  zmath  adsnasa
12. Lim C. C., “A combinatorical perturbation method and Arnold's wiskered tori in vortex dynamics”, Physica D, 64 (1993), 163–184  crossref  mathscinet  zmath  adsnasa
13. Lim C. C., “Graph theory and special class of symplectic transformations: the generalized Jacobi variables”, J. Math. Phys., 32:1 (1991), 1–7  crossref  mathscinet  zmath  adsnasa  isi
14. Newton P. K., The $N$-Vortex problem. Analytical Techniques, Springer, 2001  mathscinet


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