Abstract

Consider a linear group G acting naturally on n-dimensional real or complex space. An ordinary differential equation that is symmetric with respect to G must admit certain invariant sets, which we call invariant sets forced by symmetry. Such invariant sets can be characterized completely for any linear group, and explicitly determined for many relevant groups.

This talk is about ongoing joint work with F.D. Grosshans (West Chester) and J. Scheurle (Munich).