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Journal of Lie Theory 13 (2003), No. 1, 279--289
Copyright Heldermann Verlag 2003

Local Integrating Factors

Sebastian Walcher
Lehrstuhl A für Mathematik, RWTH Aachen, 52056 Aachen, Germany

This is an investigation of local (analytic or formal) integrating factors near certain degenerate stationary points of plane analytic vector fields. The method is to use blow-ups and then apply known results from the non-degenerate case.  The main result is that in general there is no formal integrating factor which is algebraic over the quotient field of the formal power series ring.

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