# A program to compute Birkhoff normal forms of symplectic maps in R 4

## Description

Abstract A program to compute Birkhoff normal forms for symplectic maps in R ^4 is described. We consider the case of an elliptic fixed point, which is the most relevant for applications. We compute the normal forms both in the nonresonant and resonant case and we provide the interpolating Hamiltonian and the normalizing transformation. Title of program: ARES Catalogue Id: ADAO_v1_0 Nature of problem The computation of normal forms of symplectic maps provides informations on the structure of the phase space in a neighbourhood of a fixed point. This approach can be useful in beam dynamics to analyse the effects of nonlinearities of a magnetic lattice. The normal forms allow one to analytically optimize a magnetic lattice, constructing effective correction strategies for the multipolar errors. Versions of this program held in the CPC repository in Mendeley Data ADAO_v1_0; ARES; 10.1016/0010-4655(94)00140-W This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)