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 Volume 8, Number 6, 2018, Pages 1833-1850 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. Abstract: 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. PDF      Download reader