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TY - UNPB AU - Zolkin, T. AU - Nagaitsev, S. ED - Kuzin, Maxim ED - Schaa, Volker RW TI - McMillan Map and Its Application for Accelerator Physics J2 - Proc. of RuPAC2016, St. Petersburg, Russia, November 21-25, 2016 C1 - St. Petersburg, Russia T2 - Russian Particle Accelerator Conference T3 - 25 LA - english AB - McMillan map is an important discrete time model of 1D transverse nonlinear accelerator lattice. We will discuss a full analytical theory based on parametrization of individual canonical biquadratic curves*. Using the normal forms provided in* we were able to generalize this result to entire phase-plane of finite trajectories and calculate mechanical action-angle coordinates. In addition we will present an alternative way of analytical extraction of phase-advance variable out of map's invariant of motion (Danilov Theorem). The connection of these results with possible 2D generalizations, axially symetric and 2D-magnetostatic McMillan lenses, is presented. PB - JACoW CP - Geneva, Switzerland ER -