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J. Murdock and J. A. Sanders, “A New Transvectant Algorithm for Nilpotent Normal Forms,” Journal of Differential Equations, Vol. 238, No. 1, 2007, pp. 234-256. doi:10.1016/j.jde.2007.03.016

has been cited by the following article:

• TITLE: Normal Form for Systems with Linear Part N3(n)

  AUTHORS: Grace Gachigua, David Malonza, Johana Sigey

  KEYWORDS: Transvectant; Equivariants; Box Product; Stanley Decomposition

  JOURNAL NAME: Applied Mathematics, Vol.3 No.11, November 20, 2012

  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 3 × 3 with linear nilpotent part made up of coupled R3n 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.