Splitting of separatrices in a family of area-preserving maps that unfolds a fixed point at the resonance of order three

Giannis Moutsinas

Published 2016-12-14Version 1

We study the exponentially small splitting of separatrices in an one parameter family of area-preserving maps that unfolds the 1:3 resonance. We show that under a certain non-degeneracy condition we can compute a Stokes constant $\theta$ for the map. When this constant is non zero, we provide an asymptotic for the splitting of separatrices for the map.