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. The classical technique of transforming a given vector field (describing, for example, the flow of a dynamical system ( DS)) into normal form ( NF) (in the sense of Poincar é and Dulac) is a well known and useful method of… CONTINUE READING