Dynamical systems are an essential part of the description of time
dependent processes. Because the quantitative analysis of dynamical systems
is a very complex problem, certain averaged values, the so-called
Lyapunov-exponents, were introduced to simplify these circumstances. The
Lyapunov-exponents are a measure for how much two neighbouring trajectories
drift apart from each other during the run of the dynamical system. The
amount of all Lyapunov-exponents of a system is called LCE-spectrum. It is
used for the classification of the different types of attractors and the
chaos.The aim of this paper is to research three numerical procedures for
the determination of the LCE-spectrum, to implement them practical with
Matlab and to compare them with each other. The computation methods that
are presented in this thesis are based on Gram-Schmidt orthogonalisation,
singular value decomposition and QR-factorization. Possibilities to
ascertain a suitable number of iterations and a favorable integration step
size, which are also the starting point for the comparisons, were presented
for these methods.