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Non-Collision Singularities in the Planar Two-Center-Two-Body Problem (2016)

Springer

In: Communications in Mathematical Physics

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Publication Date: 2016-07-07

Description: 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 \({\mu\ll 1}\) . 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 Painlevé conjecture.

Print ISSN: 0010-3616

Electronic ISSN: 1432-0916

Topics: Mathematics , Physics

Published by Springer

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