# name
Invariant manifolds near L1 and L2 in the Sun–Jupiter elliptic restricted three-body problem I

# metadata.dc.description.abstract[].value
In this paper, we present a way of combining the computation of invariant tori and their stable and unstable manifolds with the multiple shooting technique. We start by showing some of the results of Jorba (Nonlinearity 14(5):943–976, 2001) that should be modified in order to introduce the multiple shooting technique in these computations. After that, by a direct application in the planar elliptic restricted three-body problem (PERTBP), how to modify the equations and methods to compute the above-mentioned objects is introduced. In particular, the structure of the (systems of) equations and matrices involved in these computations is shown. An application of these computations can be found in Duarte and Jorba (Invariant manifolds of tori near and in the planar elliptic restricted three-body problem II. The Dynamics of Comet Oterma, Preprint 2023), where the dynamics of comet 39P/Oterma is modelled as a PERTBP.

# metadata.dc.relation.ispartof[].value
Celestial Mechanics and Dynamical Astronomy, 2024, vol. 136, num. 4

# metadata.dc.rights[].value
	cc by (c) Duarte, Gladston et al., 2024

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Invariant manifolds near L1 and L2 in the Sun–Jupiter elliptic restricted three-body problem I

# metadata.dc.title.alternative[].value
Invariant manifolds near $L_1$ and $L_2$ in the Sun–Jupiter elliptic restricted three-body problem I