  We investigate rescaling transformations for the Vlasov-Poisson and
Euler-Poisson systems and derive in the plasma physics case Lyapunov
functionals which can be used to analyze dispersion effects. The method is also
used for studying the long time behaviour of the solutions and can be applied
to other models in kinetic theory (2-dimensional symmetric Vlasov-Poisson
system with an external magnetic field), in fluid dynamics (Euler system for
gases) and in quantum physics (Schr\"odinger-Poisson system, nonlinear
Schr\"odinger equation).
