Seminarium KMMF "Teoria Dwoistości"

We develop a constructive approach to the problem ofpolynomial first integrals for linear vector fields. As an applicationwe obtain a new proof of the theorem of Wietzenbock about finiteness ofthe number of generators of the ring of constants of a linearderivation in the polynomial ring. Moreover, we propose an alternativeapproach to the analyticity property of the normal form reduction of agerm of vector field with nilpotent linear part in a case considered byStolovich and Verstringe.