A method for reducing chaotic dynamics in four-dimensional symplectic maps is presented. The method is to reduce certain chaos measures related to the invariants of the tangent map of fixed points. This method is applied to circular accelerators, where chaotic dynamics determines the dynamic aperture, the region of long-time stable orbits. A factor of 3--4 increase in the phase-space volume of confined trajectories is obtained.
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Wan et al. (1998) studied this question.
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