Titlebook: Averaging Methods in Nonlinear Dynamical Systems; Jan A. Sanders,Ferdinand Verhulst,James Murdock Book 2007Latest edition Springer-Verlag

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Nilpotent (Classical) Normal Form,degree of sophistication. One can consider this part of normal form theory as belonging to invariant theory. Of course, this is also true for the semisimple case, but there we can usually solve the problem without any knowledge of invariant theory beyond the obvious. A good source for the background