  An algorithm for detecting 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 systems. The difficulty in
applying the algorithm to higher-dimensional systems is mainly due to the fact
that the number of the stabilising transformations grows extremely fast with
increasing system dimension. Here we analyse the properties of stabilising
transformations and propose an alternative approach for constructing a smaller
set of transformations. The performance of the new approach is illustrated on
the four-dimentional kicked double rotor map and the six-dimensional system of
three coupled Henon maps.
