  An algorithm for detecting unstable periodic orbits in chaotic systems [Phys.
Rev. E, 60 (1999), pp. 6172-6175] which combines the set of stabilising
transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78
(1997), pp. 4733-4736] with a modified semi-implicit Euler iterative scheme and
seeding with periodic orbits of neighbouring periods, has been shown to be
highly efficient when applied to low-dimensional system. The difficulty in
applying the algorithm to higher dimensional systems is mainly due to the fact
that the number of stabilising transformations grows extremely fast with
increasing system dimension. In this thesis, we construct stabilising
transformations based on the knowledge of the stability matrices of already
detected periodic orbits (used as seeds). The advantage of our approach is in a
substantial reduction of the number of transformations, which increases the
efficiency of the detection algorithm, especially in the case of
high-dimensional systems. The performance of the new approach is illustrated by
its application to the four-dimensional kicked double rotor map, a
six-dimensional system of three coupled H\'enon maps and to the
Kuramoto-Sivashinsky system in the weakly turbulent regime.
