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

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)

本摘要介绍了用于计算 ( mathbb{R}^4 ) 中辛映射的 Birkhoff 正则形式的程序。我们考虑了椭圆固定点的情况，这对于应用最为相关。我们既在非共振情况下也在共振情况下计算了正则形式，并提供了插值哈密顿量和规范变换。

程序名称：ARES
目录编号：ADAO_v1_0

问题性质：辛映射正则形式的计算提供了关于固定点邻域相空间结构的详细信息。这种方法在束动力学中可用于分析磁晶的非线性效应。正则形式允许人们从理论上优化磁晶，构建有效的多极误差校正策略。

本程序版本存放在 Mendeley Data 的 CPC 仓库中：ADAO_v1_0; ARES; 10.1016/0010-4655(94)00140-W

此程序已从贝尔法斯特女王大学（1969-2019年）的 CPC 程序库中导入。