SC 99-26 Karin Gatermann: Computer Algebra Methods for Equivariant Dynamical Systems
Abstract: 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.
Keywords: Groebner bases,
algorithmic invariant theory,
equivariant dynamics,
orbit space reduction
MSC: 68Q40, 58E09