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- W3091906543 abstract "We consider the existence of responsive tori for the completely degenerate Hamiltonian system with the following Hamiltonian which is associated with the standard symplectic structure, where λ = ±1 and n > 2, n ⩾ m ⩾ 2 are integers. With P satisfying certain non-degenerate conditions, we obtain the following results: (1) For λ = −1 and sufficiently small, responsive tori exist for each ω satisfying a weak non-resonant condition; (2) For λ = 1 and * sufficiently small, there exists a Cantor set with almost full Lebesgue measure such that responsive tori exist for each if ω satisfies a Diophantine condition. Non-existence of responsive tori are also discussed when P fails to satisfy the non-degenerate condition. Our results are directly applicable to the existence problem of quasi-periodic responsive solutions of degenerate harmonic oscillators." @default.
- W3091906543 created "2020-10-15" @default.
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- W3091906543 date "2020-10-08" @default.
- W3091906543 modified "2023-10-14" @default.
- W3091906543 title "Completely degenerate responsive tori in Hamiltonian systems" @default.
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- W3091906543 doi "https://doi.org/10.1088/1361-6544/aba093" @default.
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