Convergence of normal form transformations: The role of symmetries

Abstract

We discuss the convergence problem for coordinate transformations which take a given vector field into Poincaré-Dulac normal form. We show that the presence of linear or nonlinear Lie point symmetries can guaranteee convergence of these normalizing transformations, in a number of scenarios. As an application, we consider a class of bifurcation problems.

20 pages, no figures

References in corpus (1)

• Normal Forms, symmetry, and linearization of dynamical systems

Cited by in corpus (1)

• Normalization of rationally integrable systems