Publikationsdatum:
2016-07-07
Beschreibung:
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
Digitale ISSN:
1432-0916
Thema:
Mathematik
,
Physik
