Abstract

Given an ordinary differential equation $x\prime =f(x)$ which admits a linear symmetry group with certain properties (e.g. compact or semisimple) there is a well-known procedure to obtain a reduced vector field via group invariants. For the remaining problem, how to get back from the reduced system to the original, it seems that so far there was no systematic approach. In this talk I will show that (roughly speaking) the reconstruction of solutions for the original system involves only the solution of linear (non-autonomous) differential equations. The key ingredients are invariants of certain maximal unipotent subgroups.

Joint work with G. Gaeta, F.D. Grosshans and J. Scheurle.