In recent years, the study of the dynamics induced by the invariant manifolds
of unstable periodic orbits in nonlinear Hamiltonian dynamical systems has
led to a number of applications in celestial mechanics and dynamical
astronomy. Two applications of main current interest are i) space manifold
dynamics, i.e. the use of the manifolds in space mission design, and, in a
quite different context, ii) the study of spiral structure in galaxies. At
present, most approaches to the computation of orbits associated with
manifold dynamics (i.e. periodic or asymptotic orbits) rely either on the use
of the so-called Poincar? - Lindstedt method, or on purely numerical methods.
In the present article we briefly review an analytic method of computation of
invariant manifolds, first introduced by Moser (1958), and developed in the
canonical framework by Giorgilli (2001). We use a simple example to
demonstrate how hyperbolic normal form computations can be performed, and we
refer to the analytic continuation method of Ozorio de Almeida and
co-workers, by which we can considerably extend the initial domain of
convergence of Moser?s normal form.
Computing the Set of Epsilon-Efficient Solutions in Multiobjective Space Mission Design