Asymptotic series for the splitting of separatrices near a Hamiltonian bifurcation

Details Asymptotic series for the splitting of separatrices near a Hamiltonian bifurcation Asymptotic series for the splitting of separatrices near a Hamiltonian bifurcation

2008-06-14

arxiv.org/abs/0806.2403v1

Mathematics

Dynamical Systems

Scientific paper

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 H\'enon map (Gelfreich, Sauzin (2001)), it implies exponentially small transversality of separatrices in the area-preserving H\'enon family when the multiplicator of the fixed point is close to one.

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