Polynomial normal forms for vector fields on R-3

The present paper is devoted to studying a class of smoothly (C-infinity) f initely determined vector fields on R-3. Given any such generic local syste m of the form <(<chi>)over circle> = A chi + ..., where A is a 3 x 3 matrix , we find the minimal possible number i (A) such that the vector field is i (A)-jet determined, and we find the number mu (A) of moduli in the C-infin ity classification. we also give a list of the simplest normal forms, that is, polynomials of degree i (A) containing exactly mu (A) parameters.