English

The inverse problem of the Birkhoff-Gustavson normalization and ANFER, Algorithm of Normal Form Expansion and Restoration

Numerical Analysis 2025-10-20 v1 Numerical Analysis

Abstract

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.

Keywords

Cite

@article{arxiv.math/0009212,
  title  = {The inverse problem of the Birkhoff-Gustavson normalization and ANFER, Algorithm of Normal Form Expansion and Restoration},
  author = {Yoshio Uwano},
  journal= {arXiv preprint arXiv:math/0009212},
  year   = {2025}
}

Comments

LaTeX2.09, 19 pages