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On singular Hamiltonians: the existence of quasi-periodic solutions and nonlinear stability
Author(s):
Chjan C.
Lim
Journal:
Bull. Amer. Math. Soc.
20
(1989),
35-40.
MSC (1985):
Primary 34C28, 34D99, 70H05;
Secondary 76C05, 70F10
MathSciNet review:
955317
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Additional information
References:
- [Al] V. I. Arnold, Math, methods of classical mechanics, Springer-Verlag, Berlin and New York, 1980.
- [A2] V. I. Arnold, Russian Math. Surveys 18(5) (1963), 9.
- [C] C. Conley, Comm. Pure Appl. Math. 16 (1963), 449-467. MR 154724
- [L1] Chjan C. Lim, Singular manifolds and quasi-periodic solutions of Hamiltonians for vortex lattices, Physica D 30 (1988), 343. MR 947905
- [L2] Chjan C. Lim, Symplectic techniques for vortex N-body problems, Comm. Math. Phys. (submitted).
- [L3] Chjan C. Lim, Quasi-periodic dynamics of desingularized vortex models, Physica D (1988). MR 1024401
- [L4] Chjan C. Lim, On Hamiltonian singularities and applications, Proc. of the Int'l Conf. on Theory and Applications of Diff. Eqns., March 21-25, 1988, Columbus, Ohio. MR 1026211
- [M1] J. Moser, Stable and random motions in dynamical systems, Princeton Univ. Press, Princeton, N.J., 1973. MR 442980
- [M2] J. Moser, Nachr. Akad. Wiss. Gott. Math. Phys. Kl. 2 (1982), 1.
- [M3] J. Moser, Comm. Pure Appl. Math. 23 (1970), 609-636. MR 269931
- [MO] G. Joyce and D. Montgomery, J. Plasma Phys. 10 (1973), 107.
- [MS] K. Meyer and D. Schmidt, J. Differential Equations 62 (1986), 222-336. MR 833418
- [MW] J. Marsden and A. Weinstein, Physica D 7 (1983), 305. MR 719058
- [Z] S. L. Ziglin, Dokl. Akad. Nauk SSSR 250 (1980), 1296-1300; Soviet Math. Dokl. 21 (1980), 296-299. MR 564329
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Additional Information:
DOI:
10.1090/S0273-0979-1989-15689-9
PII:
S 0273-0979(1989)15689-9
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