Geodesic
Local Integrating Factors
Sebastian Walcher1, 2, 3
1Lehrstuhl A für Mathematik, RWTH Aachen, 52056 Aachen, Germany
2This 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.
3[
Journal of Lie Theory, Tome 13 (2003) no. 1, pp. 279-289 
Sebastian Walcher. Local Integrating Factors. Journal of Lie Theory, Tome 13 (2003) no. 1, pp. 279-289. http://geodesic.mathdoc.fr/item/JOLT_2003_13_1_a16/
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     author = {Sebastian Walcher},
     title = {Local {Integrating} {Factors}},
     journal = {Journal of Lie Theory},
     pages = {279--289},
     year = {2003},
     volume = {13},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2003_13_1_a16/}
}
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Voir la notice de l'article provenant de la source Heldermann Verlag

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.