Convergence of normal form transformations: the role of symmetries
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 guarantee convergence of these normalizing
transformations in a number of scenarios. As an application, we consider a class of
bifurcation problems.
vector field into Poincaré–Dulac normal form. We show that the presence of linear or
nonlinear Lie point symmetries can guarantee convergence of these normalizing
transformations in a number of scenarios. As an application, we consider a class of
bifurcation problems.
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 guarantee convergence of these normalizing transformations in a number of scenarios. As an application, we consider a class of bifurcation problems.
Springer
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