Celestial mechanics solutions that escape (Q526042)

In this paper, the authors study the existence of a set of solutions of the spatial \(N\)-body problem that lead to escapes. The authors prove the existence a set of initial conditions through which singularity free solutions escape to infinity. They also have a multi-parameter set of singularity-free solutions, in which all particles but one escape to infinity. The proofs are based on integral equations and construction of a series solution representation on a semi-infinite interval that induces an asymptotic expansion for the solution to any order of accuracy, which converge very fast, for \(t\to\infty\) with \(N>3\) and total energy \(h\geq 0\). The calculations of the paper are performed with great detail.