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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.
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.
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