Normal Forms for Coupled Takens-Bogdanov Systems
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Date
2004
Authors
Malonza, D. M.
Journal Title
Journal ISSN
Volume Title
Publisher
Taylor & Francis
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 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.
Description
DOI: 10.2991/jnmp.2004.11.3.8
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Citation
Journal of Nonlinear Mathematical Physics Volume 11, Issue 3, 2004