Title: A spectral sequence approach to normal forms.
Authors: Martin Bendersky & Richard C. Churchill
Address: CUNY/Hunter College, Graduate Center
New York, NY 10021
AMS Classification: 55T05, 34C20
Email: mbenders@math.hunter.cuny.edu
rchurchi@math.hunter.cuny.edu
Abstract:
The theory of normal forms has been around since Poincare's time.
An incomplete list of applications are to vector fields,
Hamiltonians at equilibria, differential equations and singularity
theory. In general one tries to modify a given element in a Lie
algebra into a particularly useful form. The algorithm that
performs the conversion (the normal form algorithm) can be a
formidable computation. In this paper we generalize the notion of
normal form to that of an initially linear group representation.
In this general setting we are able to interpret the normal form
algorithm as a calculation of a particularly simple spectral
sequence. As a consequence we show that various vector spaces
that appear in the process of carrying out the normal form
algorithm are invariants of the orbit of the group representation.