A method for reducing chaotic dynamics in four-dimensional symplectic
maps is presented. The method is to reduce certain chaos measures rela
ted 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. [S0031-9007(98)07495-X].