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TY - UNPB AU - Zolkin, T. AU - Nagaitsev, S. ED - Schaa, Volker RW ED - Power, Maria ED - Shiltsev, Vladimir ED - White, Marion TI - Analytical theory for McMillan map J2 - Proc. of NAPAC2016, Chicago, IL, USA, October 9-14, 2016 C1 - Chicago, IL, USA T2 - North American Particle Accelerator Conference T3 - 3 LA - english AB - McMillan map is an important discrete time model of 1D transverse nonlinear accelerator lattice. We provide 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. The bifurcation map for canonical McMillan map including stability of fixed points is provided. In addition, we discuss the connection of these results with possible 2D generalizations - axially symetric and 2D-magnetostatic McMillan lenses. PB - JACoW CP - Geneva, Switzerland ER -