2008/08/26 by Kazuyuki Yagasaki · 1 citation
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Chaos control and synchronization #Mathematical Dynamics and Fractals
paper · doi:10.1080/14689360802263571
openalex publication_date 2008/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We consider general non-autonomous systems on infinite- and finite-time intervals and describe some properties of hyperbolic trajectories and their stable and unstable manifolds. Our definitions of hyperbolic trajectories and their stable and unstable manifolds on finite-time intervals are different from one adopted in the previous references, but still possess a desirable property as the previous one. Furthermore, we present numerical methods based on these theoretical results to compute the stable and unstable manifolds, and propose a control method to stabilize unstable hyperbolic trajectories using geometrical structures near them like the Ott, Grebogi and Yorke (OGY) chaos control method. To demonstrate our methods, we give numerical computation results for two examples: a controlled pendulum on infinite- and finite-time intervals and a simple model for a spacecraft transferring from the Earth to the Moon.