Formation of fractal structure in many-body systems with attractive   power-law potentials
  We study the formation of fractal structure in one-dimensional many-body systems with attractive power-law potentials. Numerical analysis shows that the range of the index of the power for which fractal structure emerges is limited. Dependence of the growth rate on wavenumber and power-index is obtained by linear analysis of the collisionless Boltzmann equation, which supports the numerical results. 
Hiroko Koyama, Tetsuro Konishi