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TitleAutomatic classification of normal forms
Author(s) Karin Gatermann, Reiner Lauterbach
TextK. Gatermann and R. Lauterbach (1995) Automatic classification of normal forms. Konrad-Zuse-Zentrum. Preprint SC 95-3. To appear in Nonlinear Analysis, Theory, Methods and Applications.
TypeTechnical Report, Misc
AbstractThe aim of this paper is to demonstrate a specific application of
Computer Algebra to bifurcation theory with symmetry. The classification of different bifurcation phenomena in case of several parameters is automated, based on a classification of Grobner bases of possible tangent spaces. The computations are performed in new coordinates of fundamental invariants and fundamental equivariants, with the induced weighted ordering. In order to justify the approach the theory of intrinsic modules is applied. Results for the groups D 3 ; Z 2 ; and Z 2 Theta Z 2 demonstrate that the algorithm works independent of the group and that new results are obtained.
Keywordsbifurcation theory, singularity theory, symmetry, systems with several parameters, Computer Algebra, Grobner bases
Translation No
Refereed No