Asymptotic series for the splitting of separatrices near a Hamiltonian bifurcation

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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.

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Dynamical Systems, 70K44; 70K50; 37J20

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http://salesiana.dossiersoluciones.com/handle/123456789/162975

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0806.2403
 http://arxiv.org/abs/0806.2403

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arXiv