Mel'nikov Method Revisited

    2001, Volume 6, Number 4, pp.  377-387

    Author(s): Cicogna G., Santoprete M.

    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. These peculiarities may clearly make this approach of great interest in celestial mechanics, as shown by some classical examples.
    Citation: Cicogna G., Santoprete M., Mel'nikov Method Revisited, Regular and Chaotic Dynamics, 2001, Volume 6, Number 4, pp. 377-387

    Download File
    PDF, 302.23 Kb