An algorithm to generate canonical transformations: Application to normal forms
There are two classical ways to construct symplectomorphisms (i.e. canonical transformations of mechanics): using generating functions or using Lie series. In a previous paper [Nonlinearity 12, 1299-1322 (1999; Zbl 0949.37059)] the author proposed a new one, involving the so-called primitive functions. The goal of present paper is to discuss numerical issues of this new algorithm and, much more important, to use the algorithm as a tool to study dynamical systems. As a concrete application, developed in detail and numerically implemented, is the computation of the normal form of a KAM torus for area-preserving maps. Several pictures and four appendices are included.
scientific article; zbMATH DE number 1768947
scientific article