Symbolic dynamics in the planar three-body problem

R. Moeckel

School of Mathematics, University of Minnesota

Abstract: A chaotic invariant set is constructed for the planar three-body problem. The orbits in the invariant set exhibit many close approaches to triple collision and also excursions near infinity. The existence proof is based on finding appropriate “windows” in the phase space which are stretched across one another by flow-defined Poincaré maps.

Keywords: Celestial Mechanics, three-body problem.

MSC: 70F10, 70F15, 37N05, 76Bxx