Width of homoclinic zone for quadratic maps

Vassili Gelfreich; Vincent Naudot

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arXiv · 0805.0324

Width of homoclinic zone for quadratic maps

Vassili Gelfreich·Vincent Naudot

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Abstract

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.

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Vassili Gelfreich, Vincent Naudot. 2008-05-02. Width of homoclinic zone for quadratic maps. https://arxiv.org/abs/0805.0324

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