Invariant tori in the spatial 3-body problem by averaging and reduction [ Back ]

Date:
10.03.14   
Times:
15:30 to 16:30
Place:
CRM - Auditori (C1/034)
Speaker:
Patricia Yanguas
University:
Universidad Publica de Navarra

Abstract:

We deal with the spatial three-body problem in the various regimes where the Hamiltonian is split as the sum of two Keplerian systems plus a small perturbation. By averaging over the mean anomalies, truncating higher-order terms and using singular reduction theory we get a one-degree-of-freedom Hamiltonian system. Departing from the analysis concerning the relative equilibria of this reduced system, we carry out the reconstruction of the KAM tori surrounding the motions associated to each elliptic equilibrium. The existence of fi ve-dimensional KAM tori for the spatial three-body problem is established. These tori surround various types of motions, from circular to near rectilinear, passing through coplanar or perpendicular.