%0 Journal Article
%T An improved version of Poincare-Dulac theorem for improved nilpotent normal forms
%A J. Mikram
%A F. Zinoun
%J International Journal of Mathematical Analysis
%D 2013
%I 
%X An improved version of the well-known Poincare-Dulac¡¯s normal form theoremis first proposed. It is shown that, for a nonlinear vector field, a normal formnear a singular point can always be chosen so that the number of nonlinearcomponents is at most equal to the number of Jordan blocks in the normalizedleading matrix, thus leading to the ¡°simplest¡± form in which a formal vectorfield can be written near a singular point. Within this scope, a generalizationto any dimension of an important result on normal forms of nilpotent systemsis given. This is the main result of the paper.
%K Poincare-Dulac Normal Form
%K Jordan Normal Form
%K Nilpotent Systems
%K Lie Series
%U http://www.m-hikari.com/ijma/ijma-2013/ijma-17-20-2013/zinounIJMA17-20-2013.pdf