Reduction of Poincaré normal forms
The Poincaré algorithm for reducing systems of ordinary differential equations to normal forms (near an equilibrium point) is based on considering near identity transformation of coordinates, generated by homogeneous polynomial functions, \(h_k^j\), which are chosen in such a way that nonresonant terms of the corresponding terms are eliminated. Here the same problem is studied by considering the properties of Poincaré transformations and explicit higher-order effects. Here a possibly non-unique but easily computable expression is preferable. As in the original Poincaré theory, considerations are formal in the sense that the convergence of power series used is not discussed. To help understanding the algorithm developed an example is considered.
scientific article; zbMATH DE number 1083200