Width of homoclinic zone for quadratic maps
Dynamical Systems
2008-05-06 v1
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.
Keywords
Cite
@article{arxiv.0805.0324,
title = {Width of homoclinic zone for quadratic maps},
author = {Vassili Gelfreich and Vincent Naudot},
journal= {arXiv preprint arXiv:0805.0324},
year = {2008}
}