Triple Collision in the Quasi-Homogeneous Collinear Three-Body Problem

We generalize and improve the result of F. Diacu (J. Differential Equations128(1996), 58–77) concerning the dynamics of three-points particles moving on the line under the influence of a quasihomogeneous potentialW=U+V, whereUandVare homogeneous functions of degree −a and −b, respectively. Forb>2 we found a set of positive measure of collision orbits that do not tend to form asymptotically a central configuration.