Computer Algebra Methods for Equivariant Dynamical Systems
Please always quote using this URN: urn:nbn:de:0297-zib-4140
- An introductory chapter on Groebner bases is given which also includes new results on the detection of Groebner bases for sparse polynomial systems. Algorithms for the computation of invariants and equivariants for finite groups, compact Lie groups and algebraic groups are presented and efficient implementation and time comparision are discussed. This chapter also inlcudes improvements of the computation of Noether normalisation and Stanley decomposition. These results are applied in symmetric bifurcation theory and equivariant dynamics. As preparation of the investigation of the orbit space reduction three methods are compared for solving symmetric polynomial systems exactly. The method of orbit space reduction is improved by using the Cohen-Macaulayness of the invariant ring and nested Noether normalization. Finally this is applied for a case of mode interaction in the Taylor-Couette problem.
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| Author: | Karin Gatermann |
|---|---|
| Document Type: | Habilitation |
| Tag: | Groebner bases; algorithmic invariant theory; equivariant dynamics; orbit space reduction |
| MSC-Classification: | 58-XX GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15) / 58Exx Variational problems in infinite-dimensional spaces / 58E09 Group-invariant bifurcation theory |
| Date of first Publication: | 1999/08/09 |
| Series (Serial Number): | ZIB-Report (SC-99-26) |
| ZIB-Reportnumber: | SC-99-26 |
| Published in: | Appeared: Lecture Notes in Mathematics vol. 1728, Springer 2000 |
