Journal of Lie Theory

no. 1
Local Integrating Factors
Journal of Lie Theory, Volume 13 (2003) no. 1, pp. 279-289
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.
DOI: 10.5802/jolt.303
Classification: 34C05, 34C14
Keywords: integrating factors, degenerate stationary point, blow up 
@article{JOLT_2003_13_1_a16,
     author = {S. Walcher},
     title = {Local {Integrating} {Factors}},
     journal = {Journal of Lie Theory},
     pages = {279--289},
     year = {2003},
     volume = {13},
     number = {1},
     doi = {10.5802/jolt.303},
     zbl = {1032.34030},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.303/}
}
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S. Walcher. Local Integrating Factors. Journal of Lie Theory, Volume 13 (2003) no. 1, pp. 279-289. doi: 10.5802/jolt.303

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