Width of the Homoclinic Zone in the Parameter Space for Quadratic Maps

We study several families of planar quadratic diffeomorphisms near a Bogdanov-Takens bifurcation. For each family, the skeleton of the associated bifurcation diagram can be deduced from the interpolating flow. However, a zone of chaos confined between two lines of homoclinic bifurcation that are exp...

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Bibliographic Details
Published in:Experimental mathematics 2009-01, Vol.18 (4), p.409-427
Main Authors: Gelfreich, V., Naudot, V.
Format: Article
Language:English
Subjects:
37D45
37E30
37G10
Bogdanov map
Bogdanov-Takens bifurcation
Hénon map
Primary 37D45, 37E30, 37G10
separatic splitting
splitting function
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Summary:We study several families of planar quadratic diffeomorphisms near a Bogdanov-Takens bifurcation. For each family, the skeleton of the associated 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.
ISSN:1058-6458
1944-950X
DOI:10.1080/10586458.2009.10129058