Karin Gatermann:  
Application of SAGBI-bases to Dynamics

SAGBI-bases are a tool for systematic computation with algebras.  They are a
special basis such that membership etc. may be decided algorithmically.
Typical examples of algebras are invariant rings which appear naturally in the
context of dynamical systems such as Birkhoff normal form, Liapunov-Schmidt
reduction and reduction onto center manifold with symmetry.  Everytime it is
important to find a basis of invariant polynomials of a certain degree and/or
to find a set of relevant coefficients which have to be computed.  We will show
that SAGBI bases are a most suitable tool for these tasks.