Abstract
An unstable periodic orbit in Hamiltonian systems often possesses complex conjugate eigenvalues at one or more of its orbit points. This renders the stabilization method used for controlling chaos proposed by Ott, Grebogi, and Yorke (OGY) not directly applicable to Hamiltonian systems. By introducing the notion of stable and unstable directions at each orbit point and incorporating such directions into a control scheme, we extend the original OGY method to the control of Hamiltonian chaos. Our method also includes an efficient algorithm for calculating the stable and unstable directions at each point of a given trajectory. Other issues related to controlling chaos in Hamiltonian systems are also discussed.
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