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Volume 8, Number 6, 2018, Pages 1833-1850                                                                DOI:10.11948/2018.1833
A Blow-up method to prove formal integrability for some planar differential systems
Brigita Fercec,Jaume Gine
Keywords:Saddle constants, formal first integral, invariant analytic curve.
      In this work we provide an effective method to prove the formal integrability of the resonant saddles. The method is based on the use of a blow-up and the resolution of a recurrence differential equation using induction. Using the method some open integrability problems for certain resonant saddles are solved.
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