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

Yoshio Uwano
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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.

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Yoshio Uwano. 2000-09-25. The inverse problem of the Birkhoff-Gustavson normalization and ANFER, Algorithm of Normal Form Expansion and Restoration. https://arxiv.org/abs/math/0009212

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