An approach to Mel'nikov theory in celestial mechanics.

Details An approach to Mel'nikov theory in celestial mechanics. An approach to Mel'nikov theory in celestial mechanics.

Feb 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000jmp....41..805c&link_type=abstract

Journal of Mathematical Physics, Vol. 41, No. 2, p. 805 - 815

Mathematics

Mathematical Physics

2

Celestial Mechanics: Chaos

Scientific paper

Using a completely analytic procedure - based on a suitable extension of a classical method - the authors discuss an approach to the Poincaré-Mel'nikov theory, which can be conveniently applied also to the case of nonhyperbolic critical points, and even if the critical point is located at the infinity. In this paper, they concentrate their attention on the latter case, and precisely on problems described by Kepler-type potentials in one or two degrees of freedom, in the presence of general time-dependent perturbations. It is shown that the appearance of chaos can be proved quite easily and in a direct way, without resorting to singular coordinate transformations, such as the McGehee or blowing-up transformations. Natural examples are provided by the classical Gyldén problem, originally proposed in celestial mechanics, but also of interest in different fields, and by the general three-body problem in classical mechanics.

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