Flow map parameterization methods for invariant tori in Hamiltonian systems

The goal of this paper is to present a methodology for the computation invariant tori in Hamiltonian systems combining flow map methods, parameterization and symplectic geometry. While methods reduce dimension be computed by one (avoiding Poincaré maps), cost single step derived Newton-like method proportional FFT. Symplectic properties lead some magic cancellations that make work. multiple shooting version are applied their bundles around librational equilibrium points Restricted Three Body Problem. first order approximations corresponding manifolds, commonly known as whiskers, which very important dynamical organization have applications space mission design.