This diploma-thesis deals with the numerical approximation of stable and
unstable invariant manifolds of Poincaré-maps of dynamical systems. Usually
there do exist several stable solutions for periodic forced systems. With
given initial solution there arises the question, on which of these
solutions the system tunes in. The borders of the catchment areas of stable
periodic solutions are numerically approximated with the continuation
method by Philippow. The solution behavior of periodic forced systems of
the Dimension~2 can be clarified with the help of developed Matlab-program.
The continuation algorithm ties to the research work of many years in this
field of reference and improves an already existing Pascal-program.