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Hamiltonian systems with a discrete symmetry. (English) Zbl 0438.70022

MSC:
70H05 Hamilton’s equations
70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
70F07 Three-body problems
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References:
[1] Abraham, R.; Marsden, J.: Foundations of mechanics. (1978) · Zbl 0393.70001
[2] Birkhoff, G. D.: Dynamical systems. Colloq. publ. IX (1966) · Zbl 0171.05402
[3] Laub, A.; Meyer, K. R.: Canonical form for symplectic and Hamiltonian matrices. Celestial mech. 9, 213-238 (1974) · Zbl 0316.15005
[4] Marsden, J.; Weinstein, A.: Reduction of symplectic manifolds with symmetries. Rep. math. Physics 5, 121-130 (1974) · Zbl 0327.58005
[5] Meyer, K. R.: Symmetries and integrals in mechanics. Dynamical systems, 259-272 (1973)
[6] K. R. Meyer, Periodic solutions of the N-body problem, J. Differential Equations, in press. · Zbl 0431.70021
[7] Moulton, F. R.: Periodic orbits. (1963)
[8] Polard, H.: Mathematical introduction to celestial mechanics. (1966)
[9] Weinstein, A.: Symplectic manifolds and their Lagrangian submanifolds. Adv. in math. 6, No. 3, 329-346 (1971) · Zbl 0213.48203
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