Normal Forms for Coupled Takens-Bogdanov Systems

DOI

10.2991/jnmp.2004.11.3.8How to use a DOI?

Abstract

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. 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 TakenBogdanov 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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - David Mumo Malonza
PY  - 2004
DA  - 2004/08/01
TI  - Normal Forms for Coupled Takens-Bogdanov Systems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 376
EP  - 398
VL  - 11
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2004.11.3.8
DO  - 10.2991/jnmp.2004.11.3.8
ID  - Malonza2004
ER  -