Triple collision in the quasi-homogeneous collinear three-body problem (Q1268410)

This is a generalisation and extension of a recent work by \textit{F. Diacu} [Math. Intell. 18, No. 3, 66-70 (1996; Zbl 0892.70007)]. For three point particles moving on the line under a quasi-homogeneous potential \(w= u+v\), where \(u,v\) are homogeneous functions of degree \(-a\) and \(-b\), the authors prove that for \(b>2\) there exist a set of collision orbits of positive Lebesgue measure not forming asymptotically a central configuration. For \(b=2\) the existence of a set of collision-ejected orbits of positive measure cannot be proved. The regularisation of the singularity is done according to McGehee method.