2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106452We 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.accepted by PREPattern Formation and SolitonsChaotic Dynamicstext