  We present a unified study of some aspects of quantum bicrossproduct algebras
of inhomogeneous Lie algebras, like Poincare, Galilei and Euclidean in N
dimensions. The action associated to the bicrossproduct structure allows to
obtain a nonlinear action over a new group linked to the translations. This new
nonlinear action associates a dynamical system to each generator which is the
object of study in this paper.
