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math.DS2008★ 7 cited
Asymptotic series for the splitting of separatrices near a Hamiltonian bifurcation
Vassili Gelfreich, Niklas Brannstrom
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 saddl…
math.DS2008★ 2 cited
Width of homoclinic zone for quadratic maps
Vassili Gelfreich, Vincent Naudot
We study several families of planar quadratic diffeomorphisms near a Bogdanov-Takens bifurcation. For each family, the associate bifurcation diagram can be deduced from the interpo…