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Blow-up method to prove formal integrability for planar differential systems
Keywords:Resonant saddle; 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.