Vassili Gelfreich, Vincent Naudot
Published 2008-05-02Version 1
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 interpolating flow. However, a zone of chaos confined between two lines of homoclinic bifurcation that are exponentially close to one-another is observed. The goal of this paper is to test numerically an accurate asymptotic expansion for the width of this chaotic zone for different families.
Classification of critical sets and their images for quadratic maps of the plane
Moduli spaces of quadratic maps: arithmetic and geometry
On the chaotic behavior of the Primal--Dual Affine--Scaling Algorithm for Linear Optimization
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