Spatial Symmetry in the Three-Body Problem

Quasi-periodic Solutions of the Spatial Lunar Three-body Problem

In this paper, we consider the spatial lunar three-body problem in which one body is far-away from the other two. By applying a well-adapted version of KAM theorem to Lidov-Ziglin’s global study of the quadrupolar approximation of the spatial lunar three-body problem, we establish the existence of several families of quasi-periodic orbits in the spatial lunar three-body problem.

Three - Body Problem

Cross Sections in the Three-body Problem

In Dynamical Systems, Birkho gave a clear formulation of a cross section, suggested a possible generalization to cross sections with boundary, and raised the question of whether or not such cross sections exist in the three-body problem. In this work, we explicitly develop Birkho 's notion of a generalized cross section, formulate homological necessary conditions for the existence of a cross se...

Symmetry groups and non-planar collisionless action-minimizing solutions of the three-body problem in three-dimensional space

Periodic and quasi-periodic solutions of the n-body problem can be found as minimizers of the Lagrangian action functional restricted to suitable spaces of symmetric paths. The main purpose of this paper is to develop a systematic approach to the equivariant minimization for the three-body problem in the three-dimensional space. First we give a finite complete list of symmetry groups fit to the...

Role of Chiral Symmetry in the Nuclear Many-Body Problem

The role of chiral (pion) dynamics in nuclear matter is reviewed. Contributions to the energy per particle from oneand two-pion exchange are calculated systematically, and it is demonstrated that already at order k f in the Fermi momentum, two-pion exchange produces realistic nuclear binding together with very reasonable values for the compressibility and the asymmetry energy. Further implicati...