Karin Gatermann: "Applications of SAGBI bases to dynamics"
Konrad-Zuse-Zentrum Berlin

SAGBI bases have been invented 10 years ago in order to compute with k-algebras such as invariant rings. I will report about implementation and applications in analysis, especially the theory of dynamical systems. In the theory of equivariant dynamical systems invariant rings and the module of equivariants appear in several situations such as normal form theory, Lyapunov-Schmidt reduction und center manifold reduction. Whenever these concepts are used within algorithms SAGBI bases are a very useful tool since they concentrate on some monomials by deforming the algebra into the leading monomial algebra and the module into a leading monomial module.