Cicogna G., Gaeta G.
Normal forms and nonlinear symmetries
(25K, TeX)

ABSTRACT.  We give some general theorems, and extensions of previous results, 
concerning the problem of transforming an algebra of vector fields 
into Poincar\'e normal form. By means of an unifying algebraic language, 
we show the possibility of obtaining either a "parallel" or "joint" 
normal form of the vector fields in a well definite way, which simplifies 
the construction of normal forms, providing a precise restriction on 
their structure. The application to the 
finite dimensional dynamical systems and to their Lie point symmetries is 
also discussed.