Stationary state in N-body system with power law interaction

Many self-gravitating systems often show scaling properties in their mass density, system size, velocities, and so on. In order to clarify the origin of these scaling properties, we consider the stationary state of N-body system with inverse power law interaction. As a simple case, we consider the self-similar stationary solution in the collisionless Boltzmann equation with power law potential and investigate its stability in terms of a linear symplectic perturbation. The stable scaling solutions obtained are characterized by the power index of the potential and the virial ratio of the initial state. It is suggested in general that the nonextensive system has various stable scaling solutions than those in the extensive system.