Birkhoff-Gustavson 规范化的逆问题与 ANFER——规范形展开与恢复算法
The inverse problem of the Birkhoff-Gustavson normalization and ANFER, Algorithm of Normal Form Expansion and Restoration
AI总结：
本文针对 Birkhoff-Gustavson 规范化的逆问题，提出符号计算程序 ANFER，并基于正则变换复合以数学术语阐述其流程，发现了 Bertrand 和 Darboux 可积性条件的新方面。
摘要：
在系列论文 [1-4] 中，Birkhoff-Gustavson 规范化的逆问题被提出并研究。为求解该逆问题，编写了符号计算程序 ANFER（规范形展开与恢复算法），并借助该程序发现了 Bertrand 和 Darboux 可积性条件的一个新方面（见 Uwano2000）。本文以数学术语呈现 ANFER 中的流程，该流程基于正则变换的复合而组织。
英文摘要：
In the series of papers [1-4], the inverse problem of the Birkhoff-Gustavson normalization was posed and studied. To solve the inverse problem, the symbolic-computing program named ANFER (Algorithm of Normal Form Expansion and Restoration) is written up, with which a new aspect of the Bertrand and Darboux integrability condition is found \cite{Uwano2000}. In this paper, the procedure in ANFER is presented in mathematical terminology, which is organized on the basis of the composition of canonical transformations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
