Simulation of the electron dynamics of chiral systems in CEP stabilized intense laser fields The ionization of randomly oriented chiral molecules by circularly polarized light leads to a photoelectron angular distribution (PAD) with a characteristic forward backward asymmetry along the propagation direction of the laser field. The effect is known as photoelectron circular dichroism (PECD) and has been experimentally observed for many molecules. A few years ago PECD has been experimentally observed in the multiphoton regime investigating the organic molecules camphor and fenchone. A detailed theoretical analysis of the underlying ionization process of these molecules remains challenging as too many degrees of freedom on different time scales are involved. Using numerical model systems of reduced complexity represents a computationally affordable way to model complex physical phenomena such as PECD. However modeling of the photoelectron momentum distribution (PEMD) requires at least the solution of the electronic 3D time dependent Schr¨odinger equation (TDSE) since the 3D PEMDs are needed to calculate the forward backward asymmetry. Solving the 3D TDSE is computationally demanding and the resulting 3D PEMDs are very complex and difficult to analyze. In this work the propagation direction of the electric field (z) is therefore neglected focusing on the ionization dynamics within the xy plane in which the electric field vector rotates. The molecular system is described by a 2D charge distribution lying in the xy plane consisting of three different nuclei and a single active electron. The ionization dynamics of such triatomic systems is simulated by means of various numerical models employing different approximations which are outlined in the following. By solving the electronic TDSE the time dependent electronic density at specific times and the 2D PEMD are calculated to study the ionization dynamics for both symmetric (all nuclear charges are equal) and asymmetric (all nuclear charges are differing) triatomic model systems. The results of the TDSE for model systems with different ranges of the potential orientations and internuclear distances are analyzed by means of classical trajectories (SMM) and different versions of the SFA. Circular dichroism in the angular distribution of photoelectron (CDAD) spectra are calculated via the difference of the PEMDs induced by left and right circularly polarized electric fields. The threefold structure of the PEMDs obtained by fully ab inito quantum dynamical methods is analyzed by means of classical trajectories. Its origin is traced back to three primary ionization events occurring at different tunnel exits at either of the three nuclei. For Coulomb like systems a clockwise rotation of the threefold structure was observed which is successfully reproduced by both approximative methods the CTMC method and the extended strong field approximation (SFA) [where ionization occurs via a bound superposition state consisting of the first three eigenstates]. These findings indicate that both the excited states and the long range Coulomb interaction induce the same clockwise rotation. For short range potentials and large internuclear distance a different ionization mechanism was proposed where the ionization takes place from the excited state at the nuclei from the so called ”up field site” of the electric field vector. This ionization mechanism is simulated by means of classical trajectories with modified initial conditions showing a very good agreement with TDSE simulations. Only the extended SFA is able to reproduce the results of the TDSE simulation correctly indicating the importance of excited states during ionization of systems with large internuclear distance. Additionally in this work the effect of averaging over the molecular orientation has been investigated. It was shown for symmetric systems that the threefold structure in the PEMD disappears in randomly orientated molecular arrangements and the spectrum only depends on electric field parameters such as the CEP and the pulse duration. For symmetric systems the PEMDs induced by LCP and RCP fields are mirror images of each other. The symmetry relation between both PEMDs vanishes for asymmetric nuclear configurations. The PEMDs of asymmetric Coulomb systems could only be reproduced by the CTMC method in the tunnel regime for wavelengths of λ = 3000 nm. The simulation of the PEMDs of asymmetric Coulomb systems by means of CTMC was not successful in the multiphoton regime (λ = 800 nm) as many excited states contribute to the ionization process. The averaged PEMDs and thus the CDAD spectra of the symmetric and asymmetric Coulomb like systems generally exhibit the same features indicating that the CDAD effect is primarily produced by the CEP of the laser field and not by the asymmetry of the potential. The results presented in this thesis provide an important precursor to reveal sensitive details of the ionization mechanism underlying the PECD effect. An extension of the 2D model to 3D which includes the propagation direction of the electric field and a fourth nucleus is straight forward (examples of 3D simulations can be found in the Appendix.) but exceeds the scope of this thesis.