Dynamical Systems and Quantum Bicrossproduct Algebras

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.