Symmetries of dynamical systems and convergent normal forms

TL;DR

This paper demonstrates that Lie point symmetries, combined with analytic constants of motion, can guarantee the convergence of transformations to normal forms in dynamical systems.

Contribution

It establishes conditions under which symmetries ensure the convergence of normal form transformations in dynamical systems.

Findings

Lie symmetries can ensure convergence of normal form transformations

Analytic constants of motion are crucial for convergence

Conditions for convergence are explicitly characterized

Abstract

It is shown that, under suitable conditions, involving in particular the existence of analytic constants of motion, the presence of Lie point symmetries can ensure the convergence of the transformation taking a vector field (or dynamical system) into normal form