Critical bending point in the Lyapunov localization spectra of   many-particle systems
  The localization spectra of Lyapunov vectors in many-particle systems at low density exhibit a characteristic bending behavior. It is shown that this behavior is due to a restriction on the maximum number of the most localized Lyapunov vectors determined by the system configuration and mutual orthogonality. For a quasi-one-dimensional system this leads to a predicted bending point at n_c \approx 0.432 N for an N particle system. Numerical evidence is presented that confirms this predicted bending point as a function of the number of particles N. 
Tooru Taniguchi and Gary P. Morriss