Elastic Scattering of Point Particles With Nearly Equal Masses
  We show that for n billiard particles on the line there exist three open sets in the product of phase space and the space of their masses, such that these particles exhibit exactly n-1, n over 2 respectively n+1 over 3 collisions. These open sets intersect any neighborhood of the diagonal in mass space. 
Andreas Knauf and Markus Stepan
math-ph math.MP