The two fixed centers: an exceptional integrable system (Q1766811)

The authors focus their interest on the two-dimensional problem, where the trajectory of the third body lies in a plane. In spite of the fact that there are many publications on the problem and its generalizations (a review of 22 papers is presented in the article), the phase portrait of the corresponding proper dynamical system was not constructed. Here the authors classify the trajectories into periodic and quasi-periodic ones, and identify collision orbits.