1997/11/04 by P. Schmelcher, Peter Schmelcher, F. K. Diakonos +1 · 2 citations
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #chao-dyn #nlin.CD
paper · pdf · doi:10.1103/physreve.57.2739
submitted to Physical Review E
arxiv created 1997/11/04 · openalex publication_date 1998/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a method to detect the unstable periodic orbits of a multidimensional 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 transformations the originally unstable periodic orbits are transformed into stable ones, and can consequently be detected and analyzed easily. This method 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.