Display Abstract

Title Flow reconstruction and invariant tori in the spatial three-body problem

Name Flora Sayas
Country Spain
Email flora.sayas@unavarra.es
Co-Author(s) Jes\'us F. Palaci\'an and Patricia Yanguas
Submit Time 2014-02-24 08:11:28
Special Session 111: Computational dynamics in Hamiltonian and dissipative systems
We study the spatial three-body problem (a system of nine degrees of freedom). Our approach is based on a combination of averaging techniques with reduction theory with the aim of building a reduced Hamiltonian and a reduced phase space. The averaged Hamiltonian defines a system of one degree of freedom in the reduced space whose dimension is two which is a singular space embedded in ${\mathbb R}^3$. We consider every elliptic point in the reduced phase space and reconstruct it step by step to compute the corresponding KAM invariant tori that persist in the original space ${\mathbb R}^{12}$. In the cases where the equilibria are placed on the singular points of the two-dimensional reduced phase space we need to make a local analysis around the singularities, passing to a surface with no singular points. In the process of reconstruction we define intermediate spaces and sets of variables depending on the type of motions under consideration. Due to the scale in the perturbation, the Hamiltonian is too degenerate to apply classical results of KAM theory. Thus, we use a specific result by Han, Li and Yi for this kind of systems. We find Cantor families of five-dimensional KAM tori for the spatial three-body problem.