- 02-88 Cicogna G., Santoprete M.
- Mel'nikov method revisited
Feb 26, 02
(auto. generated ps),
of related papers
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.