I'm familiar with the classification of fixed points of linear dynamical systems in two dimensions; it's readily available in many a book, as well as good ol' Wiki (Linear dynamical system - Wikipedia, the free encyclopedia).

However, what happens with higher-order systems, say, three-dimensional? In that case, you'll end up having three eigenvalues -- presumably, different combinations of their signs give rise to different fixed point types. Has this been investigated? I've looked at numerous books, and all I ever seem to find is classification for two dimensions.

Any help with finding a book/paper/URL dealing with this would be much appreciated!