Volume 17, Issue 1, March 2010, Pages 69 - 85
Stanley Decomposition for Coupled Takens–Bogdanov Systems
Authors
David Mumo Malonza
Department of Mathematics, Kenyatta University, P. O. Box 43844, 00100 Nairobi, Kenya,dmalo2004@yahoo.co.uk
Received 9 March 2009, Accepted 24 August 2009, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925110000647How to use a DOI?
- Keywords
- Normal forms; transvectants; box product; Stanley decomposition; Takens–Bogdanov systems; module of equivariants; ring of invariants
- Abstract
We use an algorithm based on the notion of transvectants from classical invariant theory in determining the form of Stanley decomposition of the ring of invariants for the coupled Takens–Bogdanov systems when the Stanley decompositions of the Jordan blocks of the linear part are known at each stage. The 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.
- Copyright
- © 2010 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - David Mumo Malonza PY - 2021 DA - 2021/01/07 TI - Stanley Decomposition for Coupled Takens–Bogdanov Systems JO - Journal of Nonlinear Mathematical Physics SP - 69 EP - 85 VL - 17 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925110000647 DO - 10.1142/S1402925110000647 ID - Malonza2021 ER -