Chaotic Behaviour of Hamiltonian Dynamical Systems. Study of a classical model of the hydrogen atom exposed to circularly polarized laser fields.

We have considered a classical model of the hydrogen atom exposed to a circularly polarized monochromatic electromagnetic wave. This model is related to similar models studied in various fields of physics, including the research in chaotic dynamics. The aim of the investigation has been to detect possible signs of stochasticity using the well established concept of Liapunov-exponents. The physical and mathematical background has been thoroughly explained and adaptions for the given problem have been made. The presented methods have been demonstrated using the H'enon-Heiles model and generalizations of it. The original problem has been simplified by a canonical transformation to the co-moving coordinate system of the lightwave. The properties of this transformation and it's quantum mechanical counterpart have been examined. Numerical methods have been used to integrate the classical equations of motion as well as the defining equations of the Liapunov exponents. In particular a time-tra..