Normal forms with exponentially small remainder : application to homoclinic connections for the reversible 0 2+ iω resonance
Abstract
In this note we explain how the normal form theorem established in [2] for analytic vector fields with a semi-simple linearization enables to prove the existence of homoclinic connections to exponentially small periodic orbits for reversible analytic vector fields admitting a 0 2+ iω resonance where the linearization is precisely not semi simple.
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