Abstract
We consider a one-dimensional non-degenerate Hamiltonian system perturbed by a periodically time dependent non-Hamiltonian vector field and show that the non-vanishing of the Mel’nikov subharmonic function is strongly related to the non-existence of an analytic integral in the perturbed system.
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Meletlidou, E. (2001). The Mel’nikov Subharmonic Function and the Non-Existence of Analytic Integrals in Non-Autonomous Systems. In: Dvorak, R., Henrard, J. (eds) New Developments in the Dynamics of Planetary Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2414-2_11
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DOI: https://doi.org/10.1007/978-94-017-2414-2_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5702-0
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