Analysis of Resonant Structures of a 4d Model of a Nonlinear Magnetic Lattice through Resonant Normal Forms

A generic four-dimensional model representing the nonlin-ear betatronic oscillations of a single particle in a magnetic lattice for hadrons is considered. The classiication of the diierent resonances is given and the computation of the corresponding normal form invariant is outlined. The analysis of the interpolating Hamiltonian of the resonant normal form allows to determine xed points, xed curves, location and width of resonances; a complete classiication of the geometrical structures of the phase space is outlined. Some numerical plots of the corresponding phase space are given.