Asymptotic series for the splitting of separatrices near a Hamiltonian bifurcation
This is a proof of an asymptotic formula which describes exponentially small splitting of separatrices in a generic analytic family of area-preserving maps near a Hamiltonian saddle-centre bifurcation. As a particular case and in combination with an earlier work on a Stokes constant for the Hénon map (Gelfreich, Sauzin (2001)), it implies exponentially small transversality of separatrices in the area-preserving Hénon family when the multiplicator of the fixed point is close to one.
math.DS↗