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

本文的目的是提出一种结合流图方法，参数化方法和辛几何的哈密顿系统中不变托里的计算方法。虽然流图方法减小了要由一个计算的花托的尺寸（避免庞加莱图），但参数化方法将派生类牛顿法的单个步骤的成本降低到与FFT的成本成比例。辛的性质导致一些使方法起作用的不可思议的抵消。该方法的多种射击形式适用于在限制三体问题的自由平衡点周围的不变托里及其不变束的计算。不变束是相应不变流形（通常称为晶须）的一阶近似值，