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

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          Abstract

          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.

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          Reference systems for splitting of separatrices

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            Nonlinear analysis with resurgent functions

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              Author and article information

              Journal
              2016-12-14
              Article
              1612.04752
              29f858b5-b6c4-4920-b019-4ef895fa20a8

              http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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              math.DS

              Differential equations & Dynamical systems
              Differential equations & Dynamical systems

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