Absolute and relative choreographies in the problem of point vortices moving on a plane

Regular and Chaotic Dynamics

Volumn 9, Issue 2, 2004, Pages 101-111

  Borisov, A V ^a   Mamaev, I S ^a   Kilin, A A ^a  

^a Institute of Computer Science   (Russian Federation)

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EID: 33646240239     PISSN: 15603547     EISSN: 14684845     Source Type: Journal    
DOI: 10.1070/RD2004v009n02ABEH000269     Document Type: Article

References (21)

1. H. Aref, N. Pomphrey. Integrable and chaotic motions of four vortices. I - The case of identical vortices. Proc. Roy. Soc. London Ser. A. 1982. V. 380. P. 359-387.
2. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev. Lie algebras in vortex dynamics and celestial mechanics-IV. Reg. & Chaot. Dyn. 1999. V. 4. No1. P. 23-50.
3. A. V. Borisov, I. S. Mamaev. Poisson structures and Lie algebras in Hamiltonian mechanics. Izhevsk: Udmurt University Press. 1999. (In Russian)
4. A. V. Borisov, I. S. Mamaev. Mathematical methods in the dynamics of vortex structures. In: Fundamental and applied problems of the vortex theory, eds. A. V. Borisov, I. S. Mamaev, M. A. Sokolovsky. Moscow-Izhevsk: ICS. 2003. P. 17-178. (In Russian)
5. C. V. L. Charlier. Die Mechanik des Himmels. Berlin: W. de Gruyter. 1927.
6. A. Chenciner, R. Montgomery. A remarkable periodic solution of the three-body problem in the case of equal masses. Annals of Mathematics. 2000. V. 152. No3. P. 881-901.
7. A. Chenciner, J. Gerver, R. Montgomery. C. Simo. Simple choreographies of N bodies: a preliminary study. In: Geometry, Mechanics, and Dynamics. Volume in honor of the 60th birthday of J. E Marsden, eds. P. Newton, P. Holmes, A. Weinstein. Springer. 2001.
8. D. N. Goryachev. On certain cases of motion of rectilinear parallel vortices. Moscow University Printing House. 1898. (In Russian)
9. K. M. Khanin. Quasi-periodic motions of vortex systems. Physica D. 1982. V. 4. P. 261-269.
10. V. V. Kozlov. Symmetries, topology, and resonances in Hamiltonian mechanics. Izhevsk, Udmurt University Press. 1995. (In Russian)
11. C. C. Lim. Graph theory and special class of symplectic transformations: the generalized Jacobi variables. J. Math. Phys. 1991. V. 32. No1. P. 1-7.
12. C. C. Lim. A combinatorial perturbation method and whiskered tori in vortex dynamics. Physica D. 1993. V. 64. No163-184. P. 1-7.
13. J. Marsden, A. Weinstein. Reduction of symplectic manifolds with symmetry. Rep. on Math. Phys. 1974. V. 5. No1. P. 121-130.
14. V. V. Meleshko, M. Yu. Konstantinov. Dynamics of vortex structures. Kiev: Naukova Dumka. 1993. (In Russian)
15. J. K. Moser. Lectures on Hamiltonian Systems. Mem. Amer. Math. Soc. 1968. V. 81. P. 1-60.
16. P. K. Newton. The N-Vortex problem. Analytical Techniques. Springer. 2001.
17. C. Simo. New families of solutions in N-body problems. Proc. ECM 2000, Barcelona
18. . Progress in Mathematics. Birkhäuser Verlag. 2000. V. 201. P. 101-115.
19. J. L. Synge. On the motion of three vortices. Can. J. Math. 1949. V. 1. P. 257-270.
20. J. J. Thomson. The Corpuscular Theory of Matter. London and Tonbridge. 1907.
21. S. L. Ziglin. Non-integrability of the problem of motion of four point vortices. Doklady AN SSSR. 1979. V. 250. No6. P. 1296-1300. (In Russian)