In this paper, we study a restricted four-body problem called the planar two-center-two-body problem. In the plane, we have two fixed centers Q (1) and Q (2) of masses 1, and two moving bodies Q (3) and Q (4) of masses . They interact via Newtonian potential. Q (3) is captured by Q (2), and Q (4) travels back and forth between two centers. Based on a model of Gerver, we prove that there is a Cantor set of initial conditions that lead to solutions of the Hamiltonian system whose velocities are accelerated to infinity within finite time avoiding all earlier collisions. This problem is a simplified model for the planar four-body problem case of the Painlev, conjecture.
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