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math.DS2023
Bounded orbits for 3 bodies in
Alain Albouy, Holger R. Dullin
We consider the Newtonian 3-body problem in dimension 4, and fix a value of the angular momentum which is compatible with this dimension. We show that the energy function cannot te…
math-ph2023
A limit of nonplanar 5-body central configurations is nonplanar
Alain Albouy, Antonio Carlos Fernandes
Moeckel (1990), Moeckel and Simó (1995) proved that, while continuously changing the masses, a 946-body planar central configuration bifurcates into a spatial central configuration…
math-ph2023★ 2 cited
How many Keplerian arcs are there between two points of spacetime?
Alain Albouy, Antonio J. Ureña
We consider the Keplerian arcs around a fixed Newtonian center joining two prescribed distinct positions in a prescribed flight time. We prove that, putting aside the "opposition c…