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