Normal form for systems with linear part N(3)n

Abstract

The concept of normal form is used to study the dynamics of non-linear systems. In this work we describe the normal form for vector fields on with linear nilpotent part made up of coupled n 3n  3 3  Jordan blocks. We use an algorithm based on the notion of transvectants from classical invariant theory known as boosting to equivariants in determining the normal form when the Stanley decomposition for the ring of invariants is known.