RATIONAL QUADRATIC-FLUX MINIMIZING CIRCLES FOR AREA-PRESERVING TWIST MAPS

By considering families of periodic pseudo-orbits on the cylindrical phase space of an area-preserving twist map, we construct curves of rational rotation number that are critical points of a non-negative error norm (the mean-square action gradient or ''quadratic flux''). Two alternative angle-parametrizations of the curves are presented and numerical evidence is given that the curves possess the property of non-intersection, thus making them candidates for a generalized action-angle representation for nonintegrable systems.