Topology of Jacobi levels with no zero velocity curves in the restricted three-body problem (Q1091833)

The authors study the topological description of the phase space and the geometrical space for the restricted three body problem for the case that the Jacobian constant is very small, namely, that the zero-velocity curve does not exist. For such a case it is possible that the third body which come from infinite collides with the other two bodies and the authors pay special attention to such a case. After regularization near collision points and addition of a two-torus at infinity the authors show that the phase space is topologically equivalent to the unique orientable [0,1]- bundle over the Klein bottle. Then the authors find a cube in geometrical coordinate system by topological transformation and a description in the phase space for orbits which are hyperbolic or parabolic and espe (or come from infinity) and which are asymptotic to periodic orbits on the torus at infinity.