Abstract:

A general methodology for the semi-analytical computation of invariant manifolds (center, stable, unstable, and combinations of them) of fixed points will be presented. It is based on algebraic manipulation of truncated, multivariate power series with double-precision coefficients. High efficiency can be attained through the use of a recursive representation of multivariate polynomials, combined with automatic differenciation methods for the composition of power series with elementary functions. In the computation of the vector field reduced to the invariant manifold, a partial normal form strategy can be carried out in order to make some submanifolds invariant.

An application will be made to the neighbourhood of a fixed point of the gravity field around the asteroid Vesta in body-fixed coordinates, in which the partial normal form strategy is used in order to separate the planar family of Lyapunov periodic orbits from the vertical one, and also to globally describe "transit" and "non-transit" trajectories (in the neighbourhood of the fixed point in which the expansions are valid).

This is a joint work with Àlex Haro and Benjamin Villac.