Geodesic
Local Integrating Factors
Journal of Lie theory, Tome 13 (2003) no. 1, pp. 279-289
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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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     author = {S. 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/JLT_2003_13_1_JLT_2003_13_1_a16/}
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S. Walcher. Local Integrating Factors. Journal of Lie theory, Tome 13 (2003) no. 1, pp. 279-289. http://geodesic.mathdoc.fr/item/JLT_2003_13_1_JLT_2003_13_1_a16/