Existence of the continuations in theN-body problem

Abstract

The method of obtaining the estimates of the maximalt-interval (ω ₋,ω ₊) on which the solution of theN-body problem exists and which is such that some fixed mutual distance (e. g.Δ ₁₂) exceeds some fixed non-negative lower bound, for allt contained in (ω ₋,ω ₊), is considered. For given masses and initial data, the increasing sequences of the numbersγ _k , each of which provides the estimateω ₊ >γ _k , are constructed. It appears that ifω ₊ = +∞, then$\gamma _k \xrightarrow[{k \to + \infty }]{} + \infty$.