P. Schmelcher et Fk. Diakonos, GENERAL-APPROACH TO THE LOCALIZATION OF UNSTABLE PERIODIC-ORBITS IN CHAOTIC DYNAMICAL-SYSTEMS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 57(3), 1998, pp. 2739-2746
We present a method to detect the unstable periodic orbits of a multid
imensional chaotic dynamical system. Our approach allows us to locate
in an efficient way unstable cycles of, in principle, arbitrary length
with a high accuracy. Based on a universal set of linear transformati
ons the originally unstable periodic orbits are transformed into stabl
e ones, and can consequently be detected and analyzed easily. This met
hod is applicable to dynamical systems of any dimension, and requires
no preknowledge with respect to the solutions of the original chaotic
system. As an example of application of our method, we investigate the
Ikeda attractor in some detail.