Efficient representation of invariant manifolds of periodic orbits in the crtbp

This paper deals with a methodology for defining and computing an analytical Fourier-Taylor series parameterisation of local invariant mani- folds associated to periodic orbits of polynomial vector fields. Following the Parameterisation Method, the functions involved in the series result by solving some linear non autonomous differential equations. Exploiting the Floquet nor- mal form decomposition, the time dependency is removed and the differential problem is rephrased as an algebraic system to be solved for the Fourier coef- ficients of the unknown periodic functions. The procedure leads to an efficient and fast computational algorithm. Motivated by mission design purposes, the technique is applied in the framework of the Circular Restricted Three Body problem and the parameterisation of local invariant manifolds for several halo orbits is computed and discussed.