Exponential stability of fast driven systems, with an application to celestial mechanics

We construct a normal form suited to fast driven systems. call so systems including actions I, angles ?, and one coordinate y, moving under the action of vector-field N depending only on I y with vanishing I-components. In absence such have been extensively investigated it is known that, after small perturbing term switched on, normalised turn exponentially variations compared size perturbation. obtain same result classical situation, additional benefit that no trapping argument needed, as denominator arises. use prove in three-body problem, level sets certain function called Euler integral short time, closely collisions.