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Mel'nikov method revisited

G. Cicogna·M. Santoprete
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Abstract

We illustrate a completely analytic approach to Mel'nikov theory, which is based on a suitable extension of a classical method, and which is parallel and -- at least in part -- complementary to the standard procedure. This approach can be also applied to some ``degenerate'' situations, as to the case of nonhyperbolic unstable points, or of critical points located at the infinity (thus giving rise to unbounded orbits, e.g. the Keplerian parabolic orbits), and it is naturally ``compatible'' with the presence of general symmetry properties of the problem.

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G. Cicogna, M. Santoprete. 2002-02-27. Mel'nikov method revisited. https://arxiv.org/abs/nlin/0202060

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