Malonza, D. M.2014-08-012014-08-012004Journal of Nonlinear Mathematical Physics Volume 11, Issue 3, 20041402-9251http://www.tandfonline.com/doi/pdf/10.2991/jnmp.2004.11.3.8http://ir-library.ku.ac.ke/handle/123456789/10836DOI: 10.2991/jnmp.2004.11.3.8The set of systems of differential equations that are in normal form with respect to a particular linear part has the structure of a module of equivariants, and is best described by giving a Stanley decomposition of that module. In this paper Groebner basis methods are used to determine a Groebner basis for the ideal of relations and a Stanley decomposition for the ring of invariants that arise in normal forms for Takens-Bogdanov systems. An algorithm developed by Murdock, is then used to produce a Stanley decomposition for the (normal form module) module of the equivariants from the Stanley decomposition for the ring of invariants.enArticle