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Lower-dimensional tori for generic Hamiltonian systems. (English) Zbl 1195.37038

Summary: For sufficient smooth nearly integrable Hamiltonian systems, an open dense set of perturbations has been constructed. And for a perturbation in this set the existence of families of lower-dimensional tori of hyperbolic, elliptic and mixed types has been proved.

MSC:

37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
37C55 Periodic and quasi-periodic flows and diffeomorphisms
70H08 Nearly integrable Hamiltonian systems, KAM theory
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[1] Bernstein, D.; Katok, A., Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonians, Invent, Math., 88, 225-225 (1987) · Zbl 0642.58040 · doi:10.1007/BF01388907
[2] Cheng, C. Q., Birkhoff-Kolmogorov-Arnold-Moeer tori in convex Hamiltonian systems, Commum. Math. Phys., 177, 529-529 (1996) · Zbl 0861.58030 · doi:10.1007/BF02099537
[3] Cheng, C. Q., Lower dimensional invariant tori in the regions of instability for nearly integrable Hamiltonian systems,Commun. Math. Phys., to apear. · Zbl 0935.70013
[4] Treshchev, D. V., Mechanism for destroying resonace tori of Hamiltonian systems, Math. USSR. Sb., 68, 181-181 (1991) · Zbl 0737.58025 · doi:10.1070/SM1991v068n01ABEH001371
[5] Meyer, K. R.; Hall, G. R., Introduction to Hamiltonian Dynamical Systems and the N-Body Problem (1992), Beijing: Science in China Press, Beijing · Zbl 0743.70006
[6] Pöschel, J., On elliptic lower dimensional tori in Hamiltonian system, Math. Z., 202, 559-559 (1989) · Zbl 0662.58037 · doi:10.1007/BF01221590
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