Mel'nikov method revisited

Details Mel'nikov method revisited Mel'nikov method revisited

2002-02-27

arxiv.org/abs/nlin/0202060v1

Regular and Chaotic Dynamics (Russia) 6, no. 4, 377-387 (2001)

Nonlinear Sciences

Chaotic Dynamics

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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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