2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/197718We present the applications of methods from nonlinear local harmonic analysis in variational framework to calculations of nonlinear motions in polynomial/rational approximations (up to any order) of arbitrary n-pole fields. Our approach is based on the methods provided possibility to work with dynamical beam/particle localization in phase space, which gives representions via exact nonlinear high-localized eigenmodes expansions and allows to control contribution to motion from each scale of underlying multiscale structure.3 pages, 2 figures, JAC2001.cls, submitted to Proc. Particle Accelerator Conference (PAC 2001), Chicago, June 18-22, 2001Accelerator PhysicsMathematical PhysicsPattern Formation and SolitonsComputational PhysicsQuantum Physicstext